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1、第 1 页 共 21 页高考数学专题复习导数目录一、有关切线的相关问题二、导数单调性、极值、最值的直接应用三、交点与根的分布1、判断零点个数2、已知零点个数求解参数范围四、不等式证明1、作差证明不等式2、变形构造函数证明不等式3、替换构造不等式证明不等式五、不等式恒成立求参数范围1、恒成立之最值的直接应用2、恒成立之分离常数3、恒成立之讨论参数范围六、函数与导数性质的综合运用第 2 页 共 21 页导数运用中常见结论(1)曲线()yf x在0 xx处的切线的斜率等于0()fx，且切线方程为000()()()yfxxxf x。(2)若可导函数()yf x在0 xx处取得极值，则0()0fx。反之
2、，不成立。(3)对于可导函数()f x，不等式()fx00（）的解集决定函数()f x的递增（减）区间。(4)函数()f x在区间 I 上递增（减）的充要条件是：xI()fx0(0)恒成立（()fx不恒为 0）.(5)函数()f x（非常量函数）在区间I 上不单调等价于()f x在区间I 上有极值，则可等价转化为方程()0fx在区间 I 上有实根且为非二重根。（若()fx为二次函数且I=R，则有0）。(6)()f x在区间I 上无极值等价于()fx在区间在上是单调函数，进而得到()fx0或()fx0在 I 上恒成立(7)若xI，()f x0恒成立，则min()f x0;若xI，()f x0恒成
3、立，则max()f x0(8)若0 xI，使 得0()fx0，则max()f x0；若0 xI，使 得0()fx0，则min()f x0.(9)设()f x与()g x的定义域的交集为D，若xD()()f xg x恒成立，则有min()()0f xg x.(10)若对11xI、22xI，12()()f xg x恒成立，则minmax()()f xg x.若对11xI，22xI，使得12()()f xg x,则minmin()()f xg x.若对11xI，22xI，使得12()()f xg x，则maxmax()()f xg x.（11）已知()f x在区间1I上的值域为A,，()g x在区间
4、2I上值域为B，若对11xI,22xI，使得1()f x=2()g x成立，则AB。(12)若三次函数f(x)有三个零点，则方程()0fx有两个不等实根12xx、，且极大值大于0，文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3
5、C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 Z
6、K2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3
7、C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 Z
8、K2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3
9、C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 Z
10、K2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8文档编码:CS4B3C4E3V1 HE2J5U9X9Z1 ZK2G5I1D6D8第 3 页 共 21 页极小值小于0.(13)证题中常用的不等式:ln1(0)xxxln+1(1)xx x（）1xex1xexln1(1)12xxxx22ln11(0)22xxxx
11、 sinxx(0 x)lnxx0)1x+文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4
12、文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6
13、K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4
14、文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6
15、K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4
16、文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6
17、K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4第 4 页 共 21 页一、有关切线的相关问题例题、【2015 高考新课标1，理 21】已知函数f（x）=31,()ln4xaxg xx.()当a为何值时，x轴为曲线()yf x的切线；【答案】（）34a跟踪练习：1、【2011 高考新课标1，理 21】已知函数ln()1axbf xxx，曲线()yf x在点(1,(1
18、)f处的切线方程为230 xy。（）求a、b的值；解：（）221(ln)()(1)xxbxfxxx由于直线230 xy的斜率为12，且过点(1,1)，故(1)1,1(1),2ff即1,1,22bab解得1a，1b。2、(2013课标全国，理21)设函数f(x)x2axb，g(x)ex(cxd)若曲线yf(x)和曲线yg(x)都过点P(0,2)，且在点P处有相同的切线y 4x2.(1)求a，b，c，d的值；解：(1)由已知得f(0)2，g(0)2，f(0)4，g(0)4.而f(x)2xa，g(x)ex(cxdc)，故b 2，d2，a4，dc4.从而a4，b2，c2，d 2.3、(2014 课标全
19、国，理 21)设函数1(0lnxxbef xaexx，曲线()yf x在点（1，(1)f处的切线为(1)2ye x.()求,a b；【解析】：()函数()f x的定义域为0,，112()lnxxxxabbfxaexeeexxx文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S
20、5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP
21、6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S
22、5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP
23、6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S
24、5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP
25、6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4第 5 页 共 21 页由题意可得(1)2,(1)ffe1,2ab 6 分二、导数单调性、极值、最值的直接应用（一）单调性1、根据导数
26、极值点的相对大小进行讨论例题：【2015 高考江苏，19】已知函数),()(23Rbabaxxxf.（1）试讨论)(xf的单调性；【答案】（1）当0a时，fx在,上单调递增；当0a时，fx在2,3a，0,上单调递增，在2,03a上单调递减；当0a时，fx在,0，2,3a上单调递增，在20,3a上单调递减当0a时，2,0,3ax时，0fx，20,3ax时，0fx，所以函数fx在,0，2,3a上单调递增，在20,3a上单调递减练习：1、已知函数1()ln1af xxaxx()aR.文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY
27、6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E
28、4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY
29、6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E
30、4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY
31、6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E
32、4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY
33、6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4第 6 页 共 21 页当12a时，讨论()f x的单调性；答案：1()ln1(0)af xxaxxx，222l11()(0)aaxxafxaxxxx令2()1(0)h xaxxa x当0a时，()1(0)h xxx，当(0,1),()0,()0 xh xfx,函数()f x单调递减；当(1,),()0,()0 xh xfx，函数()f x单调递增.当0a时，由()0fx，即210axxa，解得1211,1xxa.当12a时12xx，()0h x恒成立，此时()0fx，函数
34、()fx单调递减；当102a时，1110a,(0,1)x时()0,()0h xfx，函数()f x单调递减；1(1,1)xa时，()0,()0h xfx，函数()f x单调递增；1(1,)xa时，()0,()0h xfx，函数()f x单调递减.当0a时110a，当(0,1),()0,()0 xh xfx,函数()fx单调递减；当(1,),()0,()0 xh xfx，函数()f x单调递增.综上所述：当0a时，函数()f x在(0,1)单调递减，(1,)单调递增；当12a时12xx,()0h x恒成立,此时()0fx，函数()f x在(0,)单调递减；当102a时,函数()f x在(0,1)
35、递减,1(1,1)a递增,1(1,)a递减.2、已知 a为实数，函数()(1)exf xax，函数1()1g xax，令函数()()()F xf xg x 当0a时，求函数()F x的单调区间解：函数1()e1xaxF xax，定义域为1x xa当0a时，222222221()21()ee(1)(1)xxaaxa xaaFxaxax令()0Fx，得2221axa9 分文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D
36、8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y
37、4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D
38、8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y
39、4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D
40、8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y
41、4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D
42、8Q4E4第 7 页 共 21 页当210a，即12a时，()0Fx当12a时，函数()F x 的单调减区间为1(,)a，1(,)a 11 分当102a时，解2221axa得122121,aaxxaa121aaa，令()0Fx，得1(,)xa，11(,)xxa，2(,)xx；令()0Fx，得12(,)xxx13 分当102a时，函 数()F x的 单 调 减 区 间 为1(,)a，121(,)aaa，21(,)aa；函数()F x 单调增区间为2121(,)aaaa 15 分当210a，即12a时，由（2）知，函数()F x 的单调减区间为(,2)及(2,)2、根据判别式进行讨论例题：【201
43、5 高考四川，理21】已知函数22()2()ln22f xxaxxaxaa，其中0a.（1）设()g x是()f x的导函数，评论()g x的单调性；【答案】（1）当104a时，()g x在区间114114(0,),(,)22aa上单调递增，在区间114114(,)22aa上单调递减；当14a时，()g x在区间(0,)上单调递增.【解析】（1）由已知，函数()f x的定义域为(0,)，()()222ln2(1)ag xfxxaxx，所以222112()2()2224()2xaag xxxx.文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z
44、5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE
45、4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z
46、5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE
47、4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z
48、5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE
49、4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z
50、5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4文档编码:CP6I9Z5U5Y4 HY6K2K4Q2S5 ZE4G7D8Q4E4第 8 页 共 21 页当104a时，()g x在区间114114(0,),(,)22aa上单调递增，在区间114114(,)22aa上单调递减；当14a时，()g x在区间(0,)上单调递增.练习：已知函数()lnaf xxxx，aR（1）求函数()f x的单调区间；解：函数()f x 的定义域为(0,)2221()1axxafxxxx令()0fx，得20 xxa，记14a（）当14a时，()0fx，所以()f x 单调减区间为(0,)；5 分（）当14a