2013年高考文科 理科数学试题：函数与导数大题

2013年高考文科 理科数学试：函数与导数大题 2013年全国各省市高考文科、理科数学 函数与导数大题 1(本小题共13分)(2013北京.理) lnxl设为曲线在点处的切线( Cy:,(1,0)x l(?)求的方程; Cl(?)证明:除切点之外，曲线在直线的下方( (1,0) ln1lnxx,,,l解:(I),所以的斜率 ky,,1？yy,？,x,12xx l所以的方程为 yx,,1 (II)证明:令 fxxxxx()(1)ln(0),,,, 1(21)(1)xx，,,则 fxx()21,,,,xx 在(0，1)上单调递减，在(1，+?)上单调递增，又 ？fx()f(1)0, lnx时，，即,,x1 x,(0,1)fx()0,x lnx,,x1时，，即 x,，,(1,)fx()0,x l即除切点(1，0)之外，曲线C在直线的下方 22((13分)(2013•北京.文)已知函数 fxxxxx()sincos,，， b(1)若曲线在点处与直线相切，求与的值; ayfx,()(,())afayb, b(2)若曲线与直线有两个不同交点，求的取值范围( yfx,()yb, ,解:(1),因为曲线在点处与直线fxxxx()2cos,，yfx,()(,())afayb,相切， ,2cos0aaa，,faa()00,,,,,,,所以故ab,,0,1 ,,,2fabb()1,,aaaab，，,sincos,,, ,(2)？fxxx()(2cos),， ,x,0fx()0,fx()于是当时，，故单调递增( drops of Octyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 instrument reference operation conditions photoelectric doubled tube (PMT) negative high pressure: 340V; arsenic hollow cathode lamp current: 40mA; Atomic of device height: 9mm; contains air speed 33.3 standard series inorganic arsenic determination standard series: respectively accurate draw 1 μ g/mL three price arsenic (As3+) standard using liquid 0, and 0.05, and 0.1, and 0.25, and 0.5, and 1.0mL Yu 10mL capacity bottle in the, respectively added hydrochloride (1+1) solution 4mL, Potassium iodide-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50.0, 100.0ng/mL]d C2--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--solid sample: F=10mLx25mL/4mL; Liquid sample: F=10mL. II, and silver salt method 35 principle sample in 6m01/L hydrochloride solution in the, by 70 ? water bath heating Hou, inorganic arsenic to chloride of form was extraction, by Ki, and chloride Asia Tin restore for three price arsenic, then and zinc grain and acid produced of new ecological hydrogen generated arsenic of hydrogen, by silver salt solution absorption Hou, formed red rubber State real, and standard series compared quantitative. 36 36.1 hydrochloride of reagent. ,x,0当时，，故单调递减( fx()0,fx() x,0所以当时，取得最小值， fx()f(0)1, b,1b故当时，曲线与直线有两个不同交点(故的取值范yfx,()yb, 围是( (1,)，, x2k,R3((2013广东.理)(14分)设函数(其中). fxxekx,,,1，，，， 1,，k,1(?) 当时,求函数的单调区间;(?) 当时,求函数fxk,,1，，,,2,，在上的最大值M. fx0,k，，,, k,1【解析】(?) 当时, x2xxxx,, fxxex,,,1fxexexxexxe,，,,,,,,1222，，，，，，，，，， , 令fx,0,得, x,0x,ln2，，12 , 当变化时,fxfx,的变化如下: x，，，， ,,,00,ln2ln2,，, ，，，，，，0 xln2 ,fx ，，00 ,，， 极大极小fx ，， 值 值 fx0,ln2 右表可知,函数的递减区间为,递增区间为，，，， ,,,0ln2,，,,. ，，，， xxxx,fxexekxxekxxek,，,,,,,,1222 (?), ，，，，，， ,fx,0xk,ln2令x,0,得,, ，，，，21 11,k1,，,gkkk,,ln2gkgk,,,,10令,则,所以在上递,1，，，，，，，，,,kk2,， 增, gke,,,,,ln21ln2ln0ln2kk,ln20,kk,所以,从而,所以 ，，，，，，,, ,,xk,0,ln2fx,0xk,，,ln2,fx,0所以当时,;当时,; ，，，，，，，，，，，， k3Mffkkek,,,,,max0,max1,1所以 ，，，，，，,,,, k3k,hkkek,,,，11hkkek,,3令,则, ，，，，，，，， kk,,kek,,3,kee330,,,,,令,则 ，，，， agent.solution absorption Hou, formed red rubber State real, and standard series compared quantitative. 36 36.1 hydrochloride of rerice arsenic, then and zinc grain and acid produced of new ecological hydrogen generated arsenic of hydrogen, by silver salt hree p water bath heating Hou, inorganic arsenic to chloride of form was extraction, by Ki, and chloride Asia Tin restore for t?70 x25mL/4mL; Liquid sample: F=10mL. II, and silver salt method 35 principle sample in 6m01/L hydrochloride solution in the, by solid sample: F=10mL--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50.0, 100.0ng/mL]d C2-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-de (1+1) solution 4mL, Potassium iodidesing liquid 0, and 0.05, and 0.1, and 0.25, and 0.5, and 1.0mL Yu 10mL capacity bottle in the, respectively added hydrochloridard ud series inorganic arsenic determination standard series: respectively accurate draw 1 μ g/mL three price arsenic (As3+) stanhigh pressure: 340V; arsenic hollow cathode lamp current: 40mA; Atomic of device height: 9mm; contains air speed 33.3 standarnstrument reference operation conditions photoelectric doubled tube (PMT) negative drops of Octyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 i 2 2013全国高考文科、理科数学 函数与导数专题 邓老师 113,，,,,,所以在上递减,而 ,k,,,1,,,,,130ee，，，，，，,,,,,,222,，,,,, 11,，,,所以存在使得,且当时,, ,x,0,k,0x,,1kx,,，，，，000,,,,22,，,, 1,,当时,,所以在上单调递增,在上kx,,1,k,0,kx,1,x，，，，，，，，000,,2,, 单调递减. 1171,,,，因为,,所以在上恒成立,当h10,hk,0,1he,,，,0，，，，,,,,2228,，,, k,1且仅当时取得“”. , k3综上,函数在上的最大值. fx0,kMkek,,,1，，，，,, 4((本小题满分14分)(2013广东文) 32设函数 ( ，，k,Rf(x),x,kx，x k,1(1) 当时,求函数的单调区间; f(x) k,0M(2) 当时,求函数在上的最小值和最大值( ,,mk,,kf(x) '2fxxkx,,，321，，【解析】: '2fxxx,,，,,,,,,321,41280k,1，，(1)当时 '？,fx0fxR，，，，,在上单调递增. k'2x,fxxkx,,，321k,0，，(2)当时，，其开口向上，对称轴 ，且301，，，过 2,,,,，,,4124330kkk，，，，(i)当，即 'fx,0fxkk,,，，，，,,,,,30k时，，在上单调递 k 增， -k fxmfkk,,xk,，，，，从而当时， 取得最小值 , kx,3 fxxk,,，，当时， 取得最大值 k 333Mfkkkkkk,,,,,,,,,2，，. reagent blank concentrations, measured in nanograms per millilitre (ng/ml); Mstandard series compared quantitative. 36 36.1 hydrochloride of reagent.ecological hydrogen generated arsenic of hydrogen, by silver salt solution absorption Hou, formed red rubber State real, and f newof form was extraction, by Ki, and chloride Asia Tin restore for three price arsenic, then and zinc grain and acid produced o water bath heating Hou, inorganic arsenic to chloride?od 35 principle sample in 6m01/L hydrochloride solution in the, by 70 --solid sample: F=10mLx25mL/4mL; Liquid sample: F=10mL. II, and silver salt meth--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--.0, 100.0ng/mL]d C2containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-.0mL Yu 10mL capacity bottle in the, respectively added hydrochloride (1+1) solution 4mL, Potassium iodideand 1 respectively accurate draw 1 μ g/mL three price arsenic (As3+) standard using liquid 0, and 0.05, and 0.1, and 0.25, and 0.5,40mA; Atomic of device height: 9mm; contains air speed 33.3 standard series inorganic arsenic determination standard series: rent: reference operation conditions photoelectric doubled tube (PMT) negative high pressure: 340V; arsenic hollow cathode lamp curctyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 instrument drops of O 3 2,,,,，,,4124330kkk(ii)当，即时，令，，，，k,,3'2fxxkx,,，,3210，， 22kkkk，,,,33kxx,,,0解得:,注意到, xx,,,211233 12kxx,,xxk，,,kxx,,,0(注:可用韦达定理判断，,从而;12122133或者由对称结合图像判断) ？,,,mfkfxMfkfxmin,,max,，，，，，，，，,,,, 12 322？fxfkxkxxkxkx,,,，,,,，,10，，，，，，，， 111111 ？fxmfkk,,，，，，的最小值, 232322？fxfkxkxxkkkkxkxkk,,,,，,,,,,，,，，,=[1]0，，，，，，，，，， 222222 3？fxMfkkk,,,,,2，，，，的最大值 fxmfkk,,k,0，，，，综上所述，当时，的最小值,最大值 3Mfkkk,,,,,2，， k,0,,,xkk,解法2(2)当时，对，都有,, 32332fxfk,，故 fxfkxkxxkkkxxk()()(1)()0,,,，,，,,，,,，，，， 32332222fxfkxkxxkkkxkxkxkxkxkk()()()(221)()[()1]0,,,,，，，，,，,，，,，,，，, 3fxfk,,故，而 ， fkk()0,,fkkk()20,,,,,，，，， 3fxfkk()(),,所以 ， fxfkkk()()2,,,,,minmax 325((2013大纲版.文)(12分)已知函数 fxxaxx()331,，，， a,,2(1)求当时,讨论fx()的单调性; a(1)若x,，,[2,)时,fx()0,,求的取值范围. 32a,,2 解:(1)求当时, fxxaxx()331,，，， 2,,x,，21，令或 fxxx()3623,,，fxx()021,,,, agent.solution absorption Hou, formed red rubber State real, and standard series compared quantitative. 36 36.1 hydrochloride of rerice arsenic, then and zinc grain and acid produced of new ecological hydrogen generated arsenic of hydrogen, by silver salt hree p water bath heating Hou, inorganic arsenic to chloride of form was extraction, by Ki, and chloride Asia Tin restore for t?70 x25mL/4mL; Liquid sample: F=10mL. II, and silver salt method 35 principle sample in 6m01/L hydrochloride solution in the, by solid sample: F=10mL--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50.0, 100.0ng/mL]d C2-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-de (1+1) solution 4mL, Potassium iodidesing liquid 0, and 0.05, and 0.1, and 0.25, and 0.5, and 1.0mL Yu 10mL capacity bottle in the, respectively added hydrochloridard ud series inorganic arsenic determination standard series: respectively accurate draw 1 μ g/mL three price arsenic (As3+) stanhigh pressure: 340V; arsenic hollow cathode lamp current: 40mA; Atomic of device height: 9mm; contains air speed 33.3 standarnstrument reference operation conditions photoelectric doubled tube (PMT) negative drops of Octyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 i 4 2013全国高考文科、理科数学 函数与导数专题 邓老师 ,当时， ,单调递增， fx()0,fx()x,,,,(,21) ,当时， ,单调递减， fx()0,fx()x,,，(21,21) ,当时， ,单调递增; fx()0,fx()x,，，,(21,) 55(2)由，可解得，当时， ax,,,，,,(2,)a,,f(2)0,44 5122, fxxaxxxxx()3(21)3(1)3()(2)0,，，,,，,,,,22 所以函数在单调递增，于是当时， fx()(2,)，,x,，,[2,) fxf()(2)0,, 5综上可得，的取值范围是. [,),，,a4 6((13分)(2013•福建)已知函数 fxxaxaR()ln(),,, a,2(1)当时，求曲线在点处的切线方程; yfx,()Af(1,(1))(2)求函数的极值( fx() a,fx()1,,解:函数的定义域为， fx()(0,)，,x 2,a,2fx()1,,(1)当时，，， fxxx()2ln,,x ,因而， ff(1)1,(1)1,,, 所以曲线在点处的切线方程为 yfx,()Af(1,(1))xy，,,20 axa,fxx()1(0),,,,(2)由知: xx ,a,0?当时，，函数为上的增函数，函数无极fx()0,fx()(0,)，,fx()值; ,a,0xa,?当时，由fx()0,，解得 ,,又当xa,(0,)fx()0,xa,，,(,)fx()0,时，，当时，( standard series compared quantitative. 36 36.1 hydrochloride of reagent.ecological hydrogen generated arsenic of hydrogen, by silver salt solution absorption Hou, formed red rubber State real, and f newof form was extraction, by Ki, and chloride Asia Tin restore for three price arsenic, then and zinc grain and acid produced o water bath heating Hou, inorganic arsenic to chloride?od 35 principle sample in 6m01/L hydrochloride solution in the, by 70 .0mL Yu 10mL capacity bottle in the, respectively added hydrochloride (1+1) solution 4mL, Potassium iodidesolid sample: F=10mLx25mL/4mL; Liquid sample: F=10mL. II, and silver salt meth--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--.0, 100.0ng/mL]d C2containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50-and 1thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic- respectively accurate draw 1 μ g/mL three price arsenic (As3+) standard using liquid 0, and 0.05, and 0.1, and 0.25, and 0.5,40mA; Atomic of device height: 9mm; contains air speed 33.3 standard series inorganic arsenic determination standard series: rent: reference operation conditions photoelectric doubled tube (PMT) negative high pressure: 340V; arsenic hollow cathode lamp curctyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 instrument drops of O 5 从而函数在处取得极小值，且极小值为，无极xa,fx()faaaa()ln,,大值( a,0综上，当时，函数无极值; fx() a,0当时，函数在处取得极小值，无极大值( xa,fx()faaaa()ln,, a7((14分)(2013•福建)已知函数(为自然对数()1(),fxxaR,,，,exe的底数) (1)若曲线在点处的切线平行于轴，求的值; xayfx,()(1,(1))f (2)求函数的极值; fx() a,1k(3)当时，若直线与曲线没有公共点，求的最lykx:1,,yfx,()大值( aa,()1()1解:(1)由fxx,,，，得fx,,，又曲线在点处yfx,()(1,(1))fxxee a,？,,,,,,fae(1)010的切线平行于轴, xe a,()1fx,, (2) ， xe ,a,0?当时，，函数为上的增函数，函数无fx()0,fx()(,),,，,fx()极值; ,a,0xa,ln?当时，由，解得 fx()0, ,,又当时，，当时，( xa,,,(,ln)fx()0,xa,，,(ln,)fx()0, 在上单调递减,在上单调递增, ？fx()(,ln),,a(ln,)a，, xa,ln从而函数fx()在处取得极小值，且极小值为faa(ln)ln,，无极 大值( a,0fx()综上，当时，函数无极值; agent.solution absorption Hou, formed red rubber State real, and standard series compared quantitative. 36 36.1 hydrochloride of rerice arsenic, then and zinc grain and acid produced of new ecological hydrogen generated arsenic of hydrogen, by silver salt hree p water bath heating Hou, inorganic arsenic to chloride of form was extraction, by Ki, and chloride Asia Tin restore for t?70 x25mL/4mL; Liquid sample: F=10mL. II, and silver salt method 35 principle sample in 6m01/L hydrochloride solution in the, by solid sample: F=10mL--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50.0, 100.0ng/mL]d C2-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-de (1+1) solution 4mL, Potassium iodidesing liquid 0, and 0.05, and 0.1, and 0.25, and 0.5, and 1.0mL Yu 10mL capacity bottle in the, respectively added hydrochloridard ud series inorganic arsenic determination standard series: respectively accurate draw 1 μ g/mL three price arsenic (As3+) stanhigh pressure: 340V; arsenic hollow cathode lamp current: 40mA; Atomic of device height: 9mm; contains air speed 33.3 standarnstrument reference operation conditions photoelectric doubled tube (PMT) negative drops of Octyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 i 6 2013全国高考文科、理科数学 函数与导数专题 邓老师 a,0xa,ln当时，函数在处取得极小值，无极大值( fx()faa(ln)ln, 11a,1 (3)当时，，令 fxx,,，gxfxkxkx,,,,,，()1()()(1)(1)xxee则直线与曲线没有公共点,等价于方程在Rlykx:1,,yfx,()gx()0,上没有实数解( 11k,1假设，此时，， g()1,,，g(0)10,,1k,1k,1e 又函数的图象连续不断，由零点存在定理可知在R上至少gx()gx()0, k,1有一解，与“方程在R上没有实数解”矛盾，故( gx()0, 1k,1k又gx,,R时，，知方程在上没有实数解，所以的()0gx()0,xe 1最大值为. 8((13分)(2013•安徽)设函数 23nxxx*()1(,)，证明: fxxxRnN,,，，，，，,,？n22223n 2*x,nN,[,1](1)对每个，存在唯一的，满足fx()0,; nnn3 1*,,,xxx0(2)对于任意，由(1)中x构成数列满足( pN,,,nnp，nnn *x,0nN,证明:(1)对每个，当时，由函数 23nxxx**()1(,)fxxxRnN,,，，，，，,,？，可得 n22223n 21n,xxx,()10,，，，，,？fx，故函数在上是增函数(求得fx()(0,)，,23n 111ff,,，，，,？(1)0,(1)0，又1n222n23 22223n()()()n22112i333f,,，，，，，,,，,()1[]() ,n222n3323343,i2 standard series compared quantitative. 36 36.1 hydrochloride of reagent.ecological hydrogen generated arsenic of hydrogen, by silver salt solution absorption Hou, formed red rubber State real, and f newof form was extraction, by Ki, and chloride Asia Tin restore for three price arsenic, then and zinc grain and acid produced o water bath heating Hou, inorganic arsenic to chloride?od 35 principle sample in 6m01/L hydrochloride solution in the, by 70 -solid sample: F=10mLx25mL/4mL; Liquid sample: F=10mL. II, and silver salt meth--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--.0, 100.0ng/mL]d C2containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50-.0mL Yu 10mL capacity bottle in the, respectively added hydrochloride (1+1) solution 4mL, Potassium iodidethiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenicand 1 respectively accurate draw 1 μ g/mL three price arsenic (As3+) standard using liquid 0, and 0.05, and 0.1, and 0.25, and 0.5,40mA; Atomic of device height: 9mm; contains air speed 33.3 standard series inorganic arsenic determination standard series: rent: reference operation conditions photoelectric doubled tube (PMT) negative high pressure: 340V; arsenic hollow cathode lamp curctyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 instrument drops of O 7 2221n,,()[1()]1112n,133 ,,，,,,,,()023433,13 2根据函数的零点的判定定理，可得存在唯一的，满足x,[,1]n3 ( fx()0,nn *x,0(2)对于任意，由(1)中构成数列，当时， xxpN,,,nn n，1x， ？,,,fxfxfx()()()0？()()(),，,fxfxfxnnnnnn，，，111nnn，12(1)，n 由在上单调递增，可得 ( xxxx,,,,0fx()(0,)，,nnnnp，，1n，1 *故数列x为递减数列，即对任意的 npNxx,,0,,, ,,nnnp， 23n()()()xxxnnn由于......?， fxx()1,,，，，，，？nnn22223n 23n()()()xxx，，，npnpnp ,,，，，，，？fxx()1，，，npnpnp22223n nnnp，，，12()()()xxxnpnpnp，，，..............?， ，，，，？222，，，(1)(2)()nnnp 01,,x用?减去?并移项，利用，可得 np， kkkk，，npnpn()()()()xxxx,，，，npnnpnp xx,,，,,,,，nnp222kkk211,,，,，kknkn npnp，，11111 ,,,,,,,2kkknnpn,，(1)11knkn,，,， *xx综上可得，对于任意，由(1)中构成数列满足pN,,,nn 1,,,xx0( nnp，n 9. (本小题满分14分) (2013陕西.理) xfxx()e,,,R已知函数. agent.solution absorption Hou, formed red rubber State real, and standard series compared quantitative. 36 36.1 hydrochloride of rerice arsenic, then and zinc grain and acid produced of new ecological hydrogen generated arsenic of hydrogen, by silver salt hree p water bath heating Hou, inorganic arsenic to chloride of form was extraction, by Ki, and chloride Asia Tin restore for t?70 x25mL/4mL; Liquid sample: F=10mL. II, and silver salt method 35 principle sample in 6m01/L hydrochloride solution in the, by solid sample: F=10mL--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50.0, 100.0ng/mL]d C2-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-de (1+1) solution 4mL, Potassium iodidesing liquid 0, and 0.05, and 0.1, and 0.25, and 0.5, and 1.0mL Yu 10mL capacity bottle in the, respectively added hydrochloridard ud series inorganic arsenic determination standard series: respectively accurate draw 1 μ g/mL three price arsenic (As3+) stanhigh pressure: 340V; arsenic hollow cathode lamp current: 40mA; Atomic of device height: 9mm; contains air speed 33.3 standarnstrument reference operation conditions photoelectric doubled tube (PMT) negative drops of Octyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 i 8 2013全国高考文科、理科数学 函数与导数专题 邓老师 k (?) 若直线与的反函数的图像相切, 求实数的值; ykx,，1fx() 2x,0 (?) 设, 讨论曲线与曲线 公共点的个ymxm,,(0)yfx,() 数. fafb()()，fbfa()(),ab, (?) 设 , 比较与的大小, 并理由. 2ba, 【解析】(?) 的反函数. 设直线与相fx()g(x),lnxykx,，1g(x),lnx kx，1,lnx,00,,22,2切与点 。所以 k,eP(x,y),则,x,e,k,e1,000k,g'(x),0,x0, 2(?) 当时， 曲线与曲线 的公共点个ymxm,,(0)xm,,0,0yfx,() 2数即方程 根的个数。 f(x),mx xxxeexex(2),2()，令 由fxmxm,,,hxhx()'(),,,222xxx 则在上单调递减,这时,在上单调hx()(0,2)hxh()((2),),，,hx()(2,)，, 2ehxhh()((2),),(2).,，,,递增,这时 4 是的极小值即最小值. h(2)yhx,() 2所以对曲线与曲线 公共点的个数，讨论如下: ymxm,,(0)yfx,() 22ee0m,(0,)1m,当时,有个公共点;当,有个公共点; 44 2em,，,(,)2当有个公共点; 4 f(a)，f(b)f(b),f(a)(b,a，2),f(a)，(b,a,2),f(b),,(?) 设 2b,a2,(b,a) abba,(2)(2)(2)(2)b,a，,e，b,a,,eb,a，，b,a,,ea,,,e 2()2(),b,a,b,a xxx令,则 gxxxex()2(2),0,,，，,,,gxxexe'()1(12)1(1),，，,,,，,,--standard series compared quantitative. 36 36.1 hydrochloride of reagent.mass or volume of the sample, expressed in grams or milliliters (mL or g); Fecological hydrogen generated arsenic of hydrogen, by silver salt solution absorption Hou, formed red rubber State real, and f newof form was extraction, by Ki, and chloride Asia Tin restore for three price arsenic, then and zinc grain and acid produced o water bath heating Hou, inorganic arsenic to chloride?od 35 principle sample in 6m01/L hydrochloride solution in the, by 70 --solid sample: F=10mLx25mL/4mL; Liquid sample: F=10mL. II, and silver salt methreagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--.0, 100.0ng/mL]d C2containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-.0mL Yu 10mL capacity bottle in the, respectively added hydrochloride (1+1) solution 4mL, Potassium iodideand 1 respectively accurate draw 1 μ g/mL three price arsenic (As3+) standard using liquid 0, and 0.05, and 0.1, and 0.25, and 0.5,40mA; Atomic of device height: 9mm; contains air speed 33.3 standard series inorganic arsenic determination standard series: rent: reference operation conditions photoelectric doubled tube (PMT) negative high pressure: 340V; arsenic hollow cathode lamp curctyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 instrument drops of O 9 xx,的导函数 gx()gxxexe''()(11)0,,，,,,,, ,所以在上单调递增, gx()(0,)，, ,,且,因此在上单调递增,而 g(0)0,gxgx()0,(),(0,)，,g(0)0,所以在。 (0,)()0，,,上gx xx,0ab,gxxxe()2(2)0,，，,,,因为当时,且 b,a(b,a，2)，(b,a,2),ea ？,e,02,(b,a) fafbfbfa()()()()，,ab,,所以当时, 2ba, 10. (本小题满分14分) (2013陕西.文) x已知函数. fxx()e,,,R (?) 求的反函数的图象上图象上点处的切线方程; fx()(1,0) 12 (?) 证明: 曲线与曲线有唯一公共点. yfx,()yx,，，x12 ab，fbfa()(),,,ab,f (?) 设, 比较与的大小, 并说明理由. ,,2,,ba, 解(?). yx,，1 12y,x，x，1(?) 证明曲线与曲线有唯一公共点，过程如yfx,()2 1122xhxfxxxexxxR,,,,,,,,,()()11,,下。令则 22 xxhxexhx'()1,'(),,,hxe''()1,,,的导数且 hhh(0)0'(0)0,''(0)0,,,，，因此， x,0hxyhx''()0'(),,,当时, 单调递减; x,0hxyhx''()0'(),,,当时, 单调递增. ,,,,yhxh'()'(0)0,Ryhx,()所以 在上单调递增,最多有一个零点 agent.solution absorption Hou, formed red rubber State real, and standard series compared quantitative. 36 36.1 hydrochloride of rerice arsenic, then and zinc grain and acid produced of new ecological hydrogen generated arsenic of hydrogen, by silver salt hree p water bath heating Hou, inorganic arsenic to chloride of form was extraction, by Ki, and chloride Asia Tin restore for t?70 x25mL/4mL; Liquid sample: F=10mL. II, and silver salt method 35 principle sample in 6m01/L hydrochloride solution in the, by solid sample: F=10mL--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50.0, 100.0ng/mL]d C2-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-de (1+1) solution 4mL, Potassium iodidesing liquid 0, and 0.05, and 0.1, and 0.25, and 0.5, and 1.0mL Yu 10mL capacity bottle in the, respectively added hydrochloridard ud series inorganic arsenic determination standard series: respectively accurate draw 1 μ g/mL three price arsenic (As3+) stanhigh pressure: 340V; arsenic hollow cathode lamp current: 40mA; Atomic of device height: 9mm; contains air speed 33.3 standarnstrument reference operation conditions photoelectric doubled tube (PMT) negative drops of Octyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 i 10 2013全国高考文科、理科数学 函数与导数专题 邓老师 x,0 12所以，曲线与曲线只有唯一公共点.(证毕) y,x，x，1yfx,()(0,1)2 f(a)，f(b)f(b),f(a)(b,a，2),f(a)，(b,a,2),f(b)(?) 设 ,,2b,a2,(b,a) abba,(2)(2)(2)(2)b,a，,e，b,a,,eb,a，，b,a,,ea ,,,e2()2(),b,a,b,a x令 gxxxex()2(2),0,,，，,,, xx则 gxxexe'()1(12)1(1),，，,,,，,, xx,的导函数 gx()gxxexe''()(11)0,,，,,,,, ,所以在上单调递增, gx()(0,)，, ,,且,因此在上单调递增,而 g(0)0,gxgx()0,(),(0,)，,g(0)0,所以在。 (0,)()0，,,上gx xx,0ab,gxxxe()2(2)0,，，,,,因为当时,且 b,a(b,a，2)，(b,a,2),ea ？,e,02,(b,a) f(a)，f(b)f(b),f(a)当aesgt,()(?) 设(?)中所确定的s关于t的函数为, 证明: 当时, 2ln()1gt有 ,,5ln2t agent.solution absorption Hou, formed red rubber State real, and standard series compared quantitative. 36 36.1 hydrochloride of rerice arsenic, then and zinc grain and acid produced of new ecological hydrogen generated arsenic of hydrogen, by silver salt hree p water bath heating Hou, inorganic arsenic to chloride of form was extraction, by Ki, and chloride Asia Tin restore for t?70 x25mL/4mL; Liquid sample: F=10mL. II, and silver salt method 35 principle sample in 6m01/L hydrochloride solution in the, by solid sample: F=10mL--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50.0, 100.0ng/mL]d C2-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-de (1+1) solution 4mL, Potassium iodidesing liquid 0, and 0.05, and 0.1, and 0.25, and 0.5, and 1.0mL Yu 10mL capacity bottle in the, respectively added hydrochloridard ud series inorganic arsenic determination standard series: respectively accurate draw 1 μ g/mL three price arsenic (As3+) stanhigh pressure: 340V; arsenic hollow cathode lamp current: 40mA; Atomic of device height: 9mm; contains air speed 33.3 standarnstrument reference operation conditions photoelectric doubled tube (PMT) negative drops of Octyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 i 30 2013全国高考文科、理科数学 函数与导数专题 邓老师 解:(?)由题意可知函数的定义域为， (0,)，, 12,求导数可得 fxxxxxx()2ln(2ln1),，,,，x 1,令 fxx()0,,, e ,当变化时，的变化情况如下表: xfxfx(),() x111 (,)，,(0,) eee , fx()- 0 + fx()单调递减 极小值 单调递增 11所以函数的单调递减区间为，单调递增区间为 (,)，,fx()(0,) ee 01,,xt,0(?)证明:当时，，设， fx()0, 令， hxfxtx()()([1,)),,,，, 由(?)可知，在区间单调递增，, hx()(1,)，,ht(1)0,,, tttt22， heeette()ln(1)0,,,,, 故存在唯一的，使得成立; s,，,(1,)tfs,() s,1(?)证明:因为，由(?)知，，且， sgt,()tfs,() ln()lnlnlngtsssuus,ln从而，其中， ,,,,2lnln()ln(ln)2lnlnln2lntfsssssuu，， 2ln()1gtu0ln,,u,,要使成立，只需， 25ln2t 2te,当时，若sgte,,()，则由fs()的单调性， 2有矛盾， tfsfee,,,()() u,1ln0u,se,所以，即，从而成立， u11,FuuuFu()ln,1,(),,,,,另一方面，令 22u standard series compared quantitative. 36 36.1 hydrochloride of reagent.ecological hydrogen generated arsenic of hydrogen, by silver salt solution absorption Hou, formed red rubber State real, and f newof form was extraction, by Ki, and chloride Asia Tin restore for three price arsenic, then and zinc grain and acid produced o water bath heating Hou, inorganic arsenic to chloride?od 35 principle sample in 6m01/L hydrochloride solution in the, by 70 solid sample: F=10mLx25mL/4mL; Liquid sample: F=10mL. II, and silver salt meth--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--.0, 100.0ng/mL]d C2containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50-respectively accurate draw 1 μ g/mL three price arsenic (As3+) standard using liquid 0, and 0.05, and 0.1, and 0.25, and 0.5,thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-.0mL Yu 10mL capacity bottle in the, respectively added hydrochloride (1+1) solution 4mL, Potassium iodideand 140mA; Atomic of device height: 9mm; contains air speed 33.3 standard series inorganic arsenic determination standard series: rent: reference operation conditions photoelectric doubled tube (PMT) negative high pressure: 340V; arsenic hollow cathode lamp curctyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 instrument drops of O 31 ,令 Fuu()02,,, ,,12,,uu,2当时，，当时，， Fu()0,Fu()0, u,2故函数在处取到极大值，也是最大值， Fu()F(2)0, uu故有. Fuuu()ln0ln,,,,,22 2ln()1gt2综上可证:当时，有成立( te,,,5ln2t 27 (本小题满分14分) (2013天津.文) 3,x,，,(5),0axx,,f(x),设, 已知函数 a,,[2,0],a，332xxxx,，,a,0.,,2 (?) 证明在区间内单调递减, 在区间内单调递增; fx()(1,1),(1,)，,(?) 设曲线在点处的切线相互平行, 且yfx,()P(,())(1,2,3)xfxi,iii 1 证明. xxx,0,xx，，,x1231233 a，3323解:(I)令fxxxaxx()(0),,，,，( fxxaxx()(5)(0),,，,212 2,,,,10xfxxa()3(5),,，?，由于，从而当时，a,,[2,0]1 2,fxxaa()3(5)350,,，,,,,， 1 所以函数fx()在区间内单调递减， (1,0),1 2,fxxaxaxax()3(3)(3)(1),,，，,,,?，由于， a,,[2,0]2 ,01,,xfx()0,所以时; 2 ,x,1fx()0,fx()当时，，即函数在区间内单调递减，在区间(0,1)(1,)，,22 上单调递增( ff(0)(0),综合??及，可知:fx()在区间(1,1),内单调递减，在区间12 (1,)，,内单调递增; agent.solution absorption Hou, formed red rubber State real, and standard series compared quantitative. 36 36.1 hydrochloride of rerice arsenic, then and zinc grain and acid produced of new ecological hydrogen generated arsenic of hydrogen, by silver salt hree p water bath heating Hou, inorganic arsenic to chloride of form was extraction, by Ki, and chloride Asia Tin restore for t?70 x25mL/4mL; Liquid sample: F=10mL. II, and silver salt method 35 principle sample in 6m01/L hydrochloride solution in the, by solid sample: F=10mL--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50.0, 100.0ng/mL]d C2-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-de (1+1) solution 4mL, Potassium iodidesing liquid 0, and 0.05, and 0.1, and 0.25, and 0.5, and 1.0mL Yu 10mL capacity bottle in the, respectively added hydrochloridard ud series inorganic arsenic determination standard series: respectively accurate draw 1 μ g/mL three price arsenic (As3+) stanhigh pressure: 340V; arsenic hollow cathode lamp current: 40mA; Atomic of device height: 9mm; contains air speed 33.3 standarnstrument reference operation conditions photoelectric doubled tube (PMT) negative drops of Octyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 i 32 2013全国高考文科、理科数学 函数与导数专题 邓老师 a，3,(II)证明:由(I)可知:在区间内单调递减，在区间(0,)fx()(,0),,6 a，3内单调递减，在区间内单调递增( (,)，,6 因为曲线在点处的切线相互平行，从而Pxfxi(,())(1,2,3),yfx,()iii ,,,互不相等，且( xxx,,fxfxfx()()(),,123123 222不妨，由( xxx,,,03(5)3(3)3(3)xaxaxxaxa,，,,，,,，，12312233 a，322可得， 33(3)()0xxaxxxx,,，,,,，,2323233 a，3从而( 0,,,xx236 a，32设，则( ggxga()()(0),,,gxxaxa()3(3),,，，26 25a，2由3(5)()0xagxax,，,,,,,,， 1213 253aa，，xxx，，,,，所以， 12333 225a，35a,t,设a,，则， 32 315 ？at,,？,[2,0][,]33 231111t，2故xxxtt，，,,，,,,,,(1) 1236233 1xxx，，,,故( 1233 2x28(新课标?.理)(12分)已知函数,,fxxaxb(),，，gxecxd()(),， P若曲线yfx,()和曲线ygx,()都过点P(0,2)，且在点处有相同的切线yx,，42( (?)求abcd,,,的值; ?standard series compared quantitative. 36 36.1 hydrochloride of reagent.od 35 principle sample in 6m01/L hydrochloride solution in the, by 70 ecological hydrogen generated arsenic of hydrogen, by silver salt solution absorption Hou, formed red rubber State real, and f newof form was extraction, by Ki, and chloride Asia Tin restore for three price arsenic, then and zinc grain and acid produced o water bath heating Hou, inorganic arsenic to chloridesolid sample: F=10mLx25mL/4mL; Liquid sample: F=10mL. II, and silver salt meth--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--.0, 100.0ng/mL]d C2containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-.0mL Yu 10mL capacity bottle in the, respectively added hydrochloride (1+1) solution 4mL, Potassium iodideand 1 respectively accurate draw 1 μ g/mL three price arsenic (As3+) standard using liquid 0, and 0.05, and 0.1, and 0.25, and 0.5,40mA; Atomic of device height: 9mm; contains air speed 33.3 standard series inorganic arsenic determination standard series: rent: reference operation conditions photoelectric doubled tube (PMT) negative high pressure: 340V; arsenic hollow cathode lamp curctyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 instrument drops of O 33 x,,2k(?)若时，，求的取值范围( fxkgx()(), ,,解:(I)由题意知, fgfg(0)2,(0)2,(0)4,(0)4,,,, x,,而，故 bdadc,,,，,2,2,4,4fxxagxecxdc()2,()(),，,，， 从而; abcd,,,,4,2,2,2 2x(II)由(I)知，, fxxx()42,，，gxex()(1),， x2设， Fxkgxfxkexxx()()()2(1)42,,,，,,, xx,则 Fxkexxxke()2(2)242(2)(1),，,,,，, ,由题设得，令 Fxxkx()0ln,2,,,,,,Fk(0)01,,,12 2,(i)若1,,ke，则，从而当时，， ,,,20xxx,,(2,)Fx()0,11 ,当时，， xx,，,(,)Fx()0,1 即在上减，在上是增，故在上的最小xx,,(2,)(,)x，,Fx()fx()[2,),，,11 x,,2值为，而，故当时，， Fx()fxxx()(2)0,,，,fx()0,1111 即恒成立， fxkgx()(), 222x,,ke,(ii)若，则， Fxexee()2(2)(),，, ,从而当时，， x,,，,(2,)Fx()0, x,,2即在上是增，而，故当时，， Fx()[2,),，,f(2)0,,fx()0, 即恒成立， fxkgx()(), 2,,222ke,(i)ii若时，则， Fkeeke(2)222()0,,,，,,,, x,,2故当时，不可能成立， fxkgx()(), 2k综上，的取值范围是. [1,]e agent.solution absorption Hou, formed red rubber State real, and standard series compared quantitative. 36 36.1 hydrochloride of rerice arsenic, then and zinc grain and acid produced of new ecological hydrogen generated arsenic of hydrogen, by silver salt hree p water bath heating Hou, inorganic arsenic to chloride of form was extraction, by Ki, and chloride Asia Tin restore for t?70 x25mL/4mL; Liquid sample: F=10mL. II, and silver salt method 35 principle sample in 6m01/L hydrochloride solution in the, by solid sample: F=10mL--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50.0, 100.0ng/mL]d C2-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-de (1+1) solution 4mL, Potassium iodidesing liquid 0, and 0.05, and 0.1, and 0.25, and 0.5, and 1.0mL Yu 10mL capacity bottle in the, respectively added hydrochloridard ud series inorganic arsenic determination standard series: respectively accurate draw 1 μ g/mL three price arsenic (As3+) stanhigh pressure: 340V; arsenic hollow cathode lamp current: 40mA; Atomic of device height: 9mm; contains air speed 33.3 standarnstrument reference operation conditions photoelectric doubled tube (PMT) negative drops of Octyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 i 34 2013全国高考文科、理科数学 函数与导数专题 邓老师 x229(新课标?.文)(12分)已知函数，曲线fxeaxbxx()()4,，,, 在点处切线方程为 yfx,()(0,(0))fyx,，44 (?)求的值 ab, (?)讨论的单调性，并求的极大值( fx()fx() x2解:(?)， ？fxeaxbxx()()4,，,, x,， ？,，，,,fxeaxabx()()24 因为曲线在点处切线方程为 yfx,()(0,(0))fyx,，44 ,所以, ff(0)4,(0)4,,？,，,？,,babab4,84,4 x2(?)由(?)知，, ？fxexxx()4(1)4,，,, 1xx,fxexxxe,，,,,，, ()4(2)244(2)()2 ,x,,2令或 fxx()0ln2,,,,, ,,时，,时， ？,,,,,，,x(,2)(ln2,):fx()0,x,,,(2,ln2)fx()0,所以的单调增区间是，单调减区间是 fx()(,2),(ln2,),,,,，,(2,ln2),, ,2x,,2当时，函数取得极大值，极大值为( fx()fe(2)4(1),,, x30(新课标?.理)(12分)已知函数 fxexm()ln(),,， fx()x,0(Ι)设是的极值点，求，并讨论的单调性; mfx() m,2(?)当时，证明. fx()0, 1x,fx()x,0？fxe,,() 解:(?),是的极值点， xm， 1,？,,,,,fm(0)101. m x所以函数(1,),，,，其定义域为( fxex()ln(1),,， standard series compared quantitative. 36 36.1 hydrochloride of reagent.ecological hydrogen generated arsenic of hydrogen, by silver salt solution absorption Hou, formed red rubber State real, and f newof form was extraction, by Ki, and chloride Asia Tin restore for three price arsenic, then and zinc grain and acid produced o water bath heating Hou, inorganic arsenic to chloride?od 35 principle sample in 6m01/L hydrochloride solution in the, by 70 and 1solid sample: F=10mLx25mL/4mL; Liquid sample: F=10mL. II, and silver salt meth--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--.0, 100.0ng/mL]d C2containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50- thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-.0mL Yu 10mL capacity bottle in the, respectively added hydrochloride (1+1) solution 4mL, Potassium iodiderespectively accurate draw 1 μ g/mL three price arsenic (As3+) standard using liquid 0, and 0.05, and 0.1, and 0.25, and 0.5,40mA; Atomic of device height: 9mm; contains air speed 33.3 standard series inorganic arsenic determination standard series: rent: reference operation conditions photoelectric doubled tube (PMT) negative high pressure: 340V; arsenic hollow cathode lamp curctyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 instrument drops of O 35 x1(1)1ex，,x,. fxe(),,,xx，，11 xxx,设，则，所以在上为增gx()(1,),，,gxex()(1)1,，,gxexe()(1)0,，，, 函数， ,又时，，即; ？gx(0)0,0,？,gx()0,fx()0, ,,,,10x当时，( gxfx()0,()0,, fx()所以在上为减函数;在上为增函数; (1,0),(0,)，,(?)证明:当时，，故只需证明当mxm,,,，,2,(,)ln()ln(2)xmx，,， fx()0,m,2时( 1x,m,2fxe,,当时，函数在上为增函数，且()(2,),，,x，2 ,,,( f(1)0,,f(0)0, ,故在上有唯一实数根，且( xx,,(1,0)fx()0,(2,),，,00 ,,当时，，当时，， xx,,(2,)xx,，,(,)fx()0,fx()0,00 fx()从而当时，取得最小值( xx,0 1x0,由 fxexx,,,,，,,()0ln(2)000x，20 2(1)x，10故 fxfxx()()0,,，,,00xx，，2200 m,2综上，当时， fx()0, 2,x31(新课标?.文)(12分)己知函数 fxxe(),(?)求fx()的极小值和极大值; llx(?)当曲线yfx,()的切线的斜率为负数时，求在轴上截距的取 值范围( agent.solution absorption Hou, formed red rubber State real, and standard series compared quantitative. 36 36.1 hydrochloride of rerice arsenic, then and zinc grain and acid produced of new ecological hydrogen generated arsenic of hydrogen, by silver salt hree p water bath heating Hou, inorganic arsenic to chloride of form was extraction, by Ki, and chloride Asia Tin restore for t?70 x25mL/4mL; Liquid sample: F=10mL. II, and silver salt method 35 principle sample in 6m01/L hydrochloride solution in the, by solid sample: F=10mL--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50.0, 100.0ng/mL]d C2-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-de (1+1) solution 4mL, Potassium iodidesing liquid 0, and 0.05, and 0.1, and 0.25, and 0.5, and 1.0mL Yu 10mL capacity bottle in the, respectively added hydrochloridard ud series inorganic arsenic determination standard series: respectively accurate draw 1 μ g/mL three price arsenic (As3+) stanhigh pressure: 340V; arsenic hollow cathode lamp current: 40mA; Atomic of device height: 9mm; contains air speed 33.3 standarnstrument reference operation conditions photoelectric doubled tube (PMT) negative drops of Octyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 i 36 2013全国高考文科、理科数学 函数与导数专题 邓老师 222,,,,xxxx, 解:(?) fxxefxxexeexx()()2(2)？,？,,,, ,x,2令或 fxx()00,,, ,令; fxx()002,,,, ,x,2令或; fxx()00,,, 故函数在区间与上是减函数，在区间上是增函fx()(,0),,(2,)，,(0,2)数( 4x,0x,2所以是极小值点，极大值点，又故的极ff(0)0,(2),,fx()2e 40,小值和极大值分别为. 2e ,x20(II)设切点为，则切线方程为 (,)xxe00 ,,xx2200， yxeexxxx,,,,(2)()0000 2xx,200令 yxx,,,,,，，0(2)30xx,,2200 l因为曲线的切线的斜率为负数， yfx,() ,x20或x,2, ？,,？,exxx(2)000000 22xxx,,，，,,,，,，(2)32(2)3223当x,2时，， 000xx,,2200 当且仅当时取等号， x,，220 22xxx,,，，,,,,，,,(2)32(2)3322x,0当时，， 000xx,,2200 当且仅当时取等号，但是不符合条件，故应舍x,,22x,,,22000 去( lx综上可知:切线在轴上截距的取值范围是( [322,)，，, od 35 principle sample in 6m01/L hydrochloride solution in the, by 70 standard series compared quantitative. 36 36.1 hydrochloride of reagent.solid sample: F=10mLx25mL/4mL; Liquid sample: F=10mL. II, and silver salt methecological hydrogen generated arsenic of hydrogen, by silver salt solution absorption Hou, formed red rubber State real, and f newof form was extraction, by Ki, and chloride Asia Tin restore for three price arsenic, then and zinc grain and acid produced o water bath heating Hou, inorganic arsenic to chloride?--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--.0, 100.0ng/mL]d C2containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-.0mL Yu 10mL capacity bottle in the, respectively added hydrochloride (1+1) solution 4mL, Potassium iodideand 1 respectively accurate draw 1 μ g/mL three price arsenic (As3+) standard using liquid 0, and 0.05, and 0.1, and 0.25, and 0.5,40mA; Atomic of device height: 9mm; contains air speed 33.3 standard series inorganic arsenic determination standard series: rent: reference operation conditions photoelectric doubled tube (PMT) negative high pressure: 340V; arsenic hollow cathode lamp curctyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 instrument drops of O 37 32(本题满分14分)(2013浙江.理) 32已知a?R，函数 fxxxaxa()3333,,，,， (I)求曲线在点处的切线方程; yfx,()(1,(1))f (II)当时，求的最大值。 fx()x,[0,2] 32解:(1)因为, fxxxaxa()3333,,，,， 2,所以 fxxxa()363,,， ,故，又，所以所求的切线方程为 fa(1)33,,f(1)1,yaxa,,,，(33)34 2,(2)由于 fxxax()3(1)3(1),(02),,，,,, ,a,0故当时，有，此时在上单调递减， fx()0,fx()[0,2]故 fxffa()max(0),(2)33,,,,,max ,a,1当时，有，此时在上单调递增， fx()0,fx()[0,2]故 fxffa()max(0),(2)31,,,,,max 201,,a当时，由，得, xa,,,11xa,，,113(1)3(1)0xa,，,,12 ,所以，当xx,(0,)时，，函数单调递增; fx()0,fx()1 ,当xxx,(,)时，，函数单调递减; fx()0,fx()12 ,当xx,(,2)时，，函数单调递增( fx()0,fx()2 所以函数的极大值，极小值fx()fxaa()12(1)1,，,,1 ( fxaa()12(1)1,,,,2 fxfx()()20，,,故，( fxfxaa()()4(1)10,,,,,1212 fxfx()(),从而. 12 fxmaxfffx()(0),(2),(),所以 ,,1max agent.solution absorption Hou, formed red rubber State real, and standard series compared quantitative. 36 36.1 hydrochloride of rerice arsenic, then and zinc grain and acid produced of new ecological hydrogen generated arsenic of hydrogen, by silver salt hree p water bath heating Hou, inorganic arsenic to chloride of form was extraction, by Ki, and chloride Asia Tin restore for t?70 x25mL/4mL; Liquid sample: F=10mL. II, and silver salt method 35 principle sample in 6m01/L hydrochloride solution in the, by solid sample: F=10mL--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50.0, 100.0ng/mL]d C2-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-de (1+1) solution 4mL, Potassium iodidesing liquid 0, and 0.05, and 0.1, and 0.25, and 0.5, and 1.0mL Yu 10mL capacity bottle in the, respectively added hydrochloridard ud series inorganic arsenic determination standard series: respectively accurate draw 1 μ g/mL three price arsenic (As3+) stanhigh pressure: 340V; arsenic hollow cathode lamp current: 40mA; Atomic of device height: 9mm; contains air speed 33.3 standarnstrument reference operation conditions photoelectric doubled tube (PMT) negative drops of Octyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 i 38 2013全国高考文科、理科数学 函数与导数专题 邓老师 2当时，(又ff(0)(2),0,,a3 2aa(34), fxfaaa()(0)2(1)1(23)0,,,,,,,,12(1)123,,，,aaa 故( fxfxaa()()12(1)1,,，,,1max 2当时，，且( ,,a1ff(2)(2),,ff(2)(0),3 2aa(34),又 fxfaaa()(2)2(1)1(32),,,,,,, 2(1)13,,，aaa 23所以当时，( ,,afxf()(2),134 故( fxfxaa()()12(1)1,,，,,max1 3,,a1当时，fxf()(2),( 14 fxfa()(2)31,,,故( max , ,33(0),,aa ,3,综上所述( fxaaa()12(1)1(0),，,,,,,max4, 3,31()aa,,,,4 32aR,33(15分)(2013•浙江.文)已知，函数 fxxaxax()23(1)6,,，， a,1(?)若，求曲线在点处的切线方程; yfx,()(2,(2))f a,1[0,2]a(?)若，求在闭区间上的最小值( fx() 2,a,1, 解:(?)当时，，所以 f(2)6,fxxx()6126,,， ？f(2)4,,？曲线yfx,()在点(2,(2))f处的切线方程为yx,,68; [0,2]a(?)记ga()为fx()在闭区间上的最小值( 2, fxxaxaxxa()66(1)66(1)(),,，，,,, standard series compared quantitative. 36 36.1 hydrochloride of reagent.ecological hydrogen generated arsenic of hydrogen, by silver salt solution absorption Hou, formed red rubber State real, and f newof form was extraction, by Ki, and chloride Asia Tin restore for three price arsenic, then and zinc grain and acid produced o water bath heating Hou, inorganic arsenic to chloride?od 35 principle sample in 6m01/L hydrochloride solution in the, by 70 and 1solid sample: F=10mLx25mL/4mL; Liquid sample: F=10mL. II, and silver salt meth--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--.0, 100.0ng/mL]d C2containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50- thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-.0mL Yu 10mL capacity bottle in the, respectively added hydrochloride (1+1) solution 4mL, Potassium iodiderespectively accurate draw 1 μ g/mL three price arsenic (As3+) standard using liquid 0, and 0.05, and 0.1, and 0.25, and 0.5,40mA; Atomic of device height: 9mm; contains air speed 33.3 standard series inorganic arsenic determination standard series: rent: reference operation conditions photoelectric doubled tube (PMT) negative high pressure: 340V; arsenic hollow cathode lamp curctyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 instrument drops of O 39 ,令，得到 xxa,,1,fx()0,12 a,1当时， xa02a 1 (0,1)(1,)a(,2)aa 00 , fx() + , + 0 3 fx()单调递极大值 单调递极小值 单调递4a 31a, 2 (3),aa增 减 增 0(13),,a,2比较和的大小可得; ga(),f(0)0,faaa()(3),,,2(3)(3),,aaa, a,,1当时， x0,2a1 (0,1)(1,2),a 0 , fx() , + 0 32 fx(),,2824aa单调递减 极小值单调递增 31a, ？,,？gaafx()31() ,31(1)aa,,, ,[0,2]a在闭区间上的最小值为 gaa()0(13),,,, ,2(3)(3),,aaa, 2aR,34(13分)(2013•重庆.理)设，其中，曲fxaxx()(5)6ln,,， y线在点处的切线与轴相交于点( yfx,()(1,(1))f(0,6) a(1)确定的值; (2)求函数fx()的单调区间与极值( 62,fxaxx()2(5)(0),,，,解:(1)因为，故 fxaxx()(5)6ln,,，xagent.solution absorption Hou, formed red rubber State real, and standard series compared quantitative. 36 36.1 hydrochloride of rerice arsenic, then and zinc grain and acid produced of new ecological hydrogen generated arsenic of hydrogen, by silver salt hree p water bath heating Hou, inorganic arsenic to chloride of form was extraction, by Ki, and chloride Asia Tin restore for t?70 x25mL/4mL; Liquid sample: F=10mL. II, and silver salt method 35 principle sample in 6m01/L hydrochloride solution in the, by solid sample: F=10mL--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--containing (As3+) concentration of 0, 5.0, 10.0, 25.0, 50.0, 100.0ng/mL]d C2-thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arsenic-de (1+1) solution 4mL, Potassium iodidesing liquid 0, and 0.05, and 0.1, and 0.25, and 0.5, and 1.0mL Yu 10mL capacity bottle in the, respectively added hydrochloridard ud series inorganic arsenic determination standard series: respectively accurate draw 1 μ g/mL three price arsenic (As3+) stanhigh pressure: 340V; arsenic hollow cathode lamp current: 40mA; Atomic of device height: 9mm; contains air speed 33.3 standarnstrument reference operation conditions photoelectric doubled tube (PMT) negative drops of Octyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 i 40 2013全国高考文科、理科数学 函数与导数专题 邓老师 ,x,1令，得，所以曲线在点处的切fafa(1)16,(1)68,,,yfx,()(1,(1))f 线方程为 yaax,,,,16(68)(1) 1由切线与轴相交于点, y？,,,？,61686aaa(0,6)2 12(2)由(I)得 fxxxx()(5)6ln(0),,，,2 6(2)(3)xx,,,,x,3 ，令或 fxx()5,,，,fxx()02,,,xx ,02,,xx,3当或时，，故在，上为增函数， fx()0,fx()(0,2)(3,)，, ,23,,x当时，，故在上为减函数， fx()0,fx()(2,3) 9x,2x,3故在时取得极大值，在时取得极小值f(2)6ln2,，fx()2 . f(3)26ln3,， standard series compared quantitative. 36 36.1 hydrochloride of reagent.ecological hydrogen generated arsenic of hydrogen, by silver salt solution absorption Hou, formed red rubber State real, and f newof form was extraction, by Ki, and chloride Asia Tin restore for three price arsenic, then and zinc grain and acid produced o water bath heating Hou, inorganic arsenic to chloride-?od 35 principle sample in 6m01/L hydrochloride solution in the, by 70 solid sample: F=10mLx25mL/4mL; Liquid sample: F=10mL. II, and silver salt meth--mass or volume of the sample, expressed in grams or milliliters (mL or g); F--reagent blank concentrations, measured in nanograms per millilitre (ng/ml); M--.0, 100.0ng/mL]d C2thiourea solution lmL, 8 drops of Octyl alcohol, constant volume [the equivalent of arseniccontaining (As3+) concentration of 0, 5.0, 10.0, 25.0, 50-.0mL Yu 10mL capacity bottle in the, respectively added hydrochloride (1+1) solution 4mL, Potassium iodideand 1 respectively accurate draw 1 μ g/mL three price arsenic (As3+) standard using liquid 0, and 0.05, and 0.1, and 0.25, and 0.5,40mA; Atomic of device height: 9mm; contains air speed 33.3 standard series inorganic arsenic determination standard series: rent: reference operation conditions photoelectric doubled tube (PMT) negative high pressure: 340V; arsenic hollow cathode lamp curctyl alcohol, constant volume and mix, determination of inorganic arsenic in samples. Reagent blank at once. 33.2 instrument drops of O 41