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含参的函数单调区讨论典例(二).pdf

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1、1 导数应用：含参函数的单调性讨论(二)对函数(可求导函数)的单调性讨论可归结为对相应导函数在何处正何处负的讨论，若有多个讨论点时，要注意讨论层次与顺序，一般先根据参数对导函数类型进行分类，从简单到复杂。一、典型例题例 1、已知函数32()331,f xaxxxaR,讨论函数)(xf的单调性.分析：讨论单调性就是确定函数在何区间上单调递增，在何区间单调递减。而确定函数的增区间就是确定0)(xf的解区间；确定函数的减区间就是确定0)(xf的解区间；讨论单调性与讨论不等式的解区间相应。解：因为32()331,f xaxxxaR，所以/2()3(21)fxaxx (1)当0a时，/()3(21)fx

2、x，当1,2x时，/()0fx；当1,2x时，/()0fx；所以函数()f x在1(,2上单调递增，在1,)2上单调递减；(2)当0a时，/2()3(21)fxaxx的图像开口向上，36(1)aI)当136(1)0,aa时，时，/()0fx，所以函数()f x在 R上递增；II)当0136(1)0,aa时，时，方程/()0fx的两个根分别为121111,aaxxaa且12,xx所以函数()f x在11(,)aa，11(,)aa上单调递增，在1111(,)aaaa上单调递减；(3)当0a时，/2()3(21)fxaxx的图像开口向下，且36(1)0a方程/()0fx的两个根分别为121111,a

3、axxaa且12,xx所以函数()fx在11(,)aa，11(,)aa上单调递减，在1111(,)aaaa上单调递增。2 综上所述，当0a时，所以函数()f x在1111(,)aaaa上单调递增，在11(,)aa，11(,)aa上单调递减；当0a时，()f x在1(,2上单调递增，在1,)2上单调递减；当01a时，所以函数()f x在11(,)aa，11(,)aa上单调递增，在1111(,)aaaa上单调递减；当1a时，函数()f x在 R上递增；小结：导函数为二次型的一股先根据二次项系数分三种情况讨论（先讨论其为0 情形），然后讨论判别式（先讨论判别式为负或为0 的情形，对应导函数只有一种符

4、号，原函数在定义域上为单调的），判别式为正的情况下还要确定两根的大小（若不能确定的要进行一步讨论），最后根据导函数正负确定原函数相应单调性，记得写出综述结论。例 2（2010 山东理数改编）已知函数1()ln1afxxaxx()aR.讨论()f x的单调性；解：因为1()ln1af xxaxx的定义域为),0(所以222111()(0,)aaxxafxaxxxx，令2()1,(0,)h xaxxa x，则)()(xgxf与同号法一：根据熟知二次函数性质可知g(x)的正负符号与开口有关，因此可先分类型讨论：文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码

5、:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6

6、HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 Z

7、G10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档

8、编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O

9、6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9

10、 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7

11、文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R73 当0a时，由于110a1，)(xh开口向下,结合其图象易知(0,1)x，()0h x,此时()0fx，函数()f x单调递减；(1,)x时，()0h x，此时()0fx，函数()f x单调递增.当0a时，)(xh开口向上,但2x是否在定义域需要讨论：因10011aaa或所以i)当1a时，由于110a1，)(xh开口向上,结合其图象易知(0,1)x，

12、()0h x，此时()0fx，函数()f x单调递增.(1,)x时，()0h x,此时()0fx，函数()f x单调递减；ii)当10a时，g(x)开口向上且),0(,21xx，但两根大小需要讨论：a)当12a时，12,()0 xxhx 恒成立，此时()0fx，函数()fx在（0，+）上单调递减；b)当1101 102aa 时，g(x)开口向上且在（0，）有两根(0,1)x时，()0h x，此时()0fx，函数()f x单调递减；1(1,1)xa时()0h x，此时()0fx，函数()fx单调递增；1(1,)xa时，()0h x，此时()0fx，函数()f x单调递减；c)当121a时，111

13、0a，g(x)开口向上且在（0，）有两根)11,0(ax时，()0h x，此时()0fx，函数()f x单调递减；)1,11(ax时()0h x，此时()0fx，函数()fx单调递增；),1(x时，()0h x，此时()0fx，函数()f x单调递减；小结：此法是把单调区间讨论化归为导函数符号讨论，而确定导函数符号的分子是常见二次型的，一般要先讨论二次项系数，确定类型及开口；然后由于定义域限制讨论其根是否在定义域内，再讨论两根大小注，结合g(x)的图象确定其在相应区间的符号，得出导函数符号。讨论要点与解含参不等式的讨论相应。文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9

14、A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM

15、7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9

16、L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10

17、A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:

18、CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 H

19、I9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG

20、10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R74 法二：10011aaa或i)当0a时，由于110a1，)(xh开口向下,结合其图象易知(0,1)x，()0h x,此时()0fx，函数()f x单调递减；(1,)x时，()0h x，此时()0fx，函数()f x单调递增.ii)当1a时，由于11 0a0)令2()2(1)2(1)1g xaa xa x,则)(xf与)(xg同号（

21、1）当1a时，xxfxxfxgln)(,01)(,1)(在定义域),0(上为增函数(2)当1a时,224(1)8(1)121644(31)(1)aaaaaaa当0113a时，g(x)开口向上，图象在x 轴上方，所以0)(xg所以()0fx，则()f x在(0,)上单调递增当0131aa或,此时令()0fx，解得)1(21,)1(2121aaaxaaax由于210)(100)1(2xxxgaaa开口向上且，因此可进一步分类讨论如下：i)当1a时，120)(0)1(2x，xxgaa开口向下文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3

22、O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S

23、9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R

24、7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4

25、S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T

26、2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R

27、9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5

28、O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R76 0 x，()0fx10 xx;()0fx1xx则()f x在1(31)(1)(0,)2(1)aaaaa上单调递增，在1(31)(1)(,)2(1)aaaaa上单调递减ii)当103a时，()0fx10 xx或2xx;()0fx21xxx则()fx在1(31)(1)(0,)2(1)aaaaa，1(31)(1)(,)2(1)aaaaa上单调递增，在1(31)(1)1(31

29、)(1)(,)2(1)2(1)aaaaaaaaaa上单调递减综上所述，f(x)的单调区间根据参数a讨论情况如下表：103a113a1a1(0,)x12(,)x x2(,)x(0,)1(0,)x1(,)x增减增增增增（其中12(1)(31)(1)(31)11,22(1)22(1)aaaaxxaaaaaa)小结：求单调区间要确定定义域，确定导函数符号的关键是看分子相应函数，因此讨论点有：第一是类型（一次与二次的根个数显然不同)；第二有没有根（二次的看判别式），第三是有根是否为增根（在不在定义根内；第四有根的确定谁大；第五看区间内导函数的正负号（二次函数要看开口）。确记要数形结合，多数考题不

30、会全部讨论点都要讨论的，题中往往有特别条件，不少讨论点会同时确定（即知一个就同时确定另一个）。判别式与开口的讨论点先谁都可以，但从简单优先原则下可先根据判别式讨论，因为当导函数无根时它只有一种符号，相应原函数在定义域内（每个连续的区间）为单调函数较简单。文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y

31、5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6

32、U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9

33、A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM

34、7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9

35、L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10

36、A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R77 二、巩

37、固作业：1.已知函数()ln.af xxx，求()f x的单调区间.解：221+,axafxxxx函数的定义域为（0，），0fxxa令得：000,(0,)000,0(,)aaffxaafffxa若即，则x在上单调递增；若即，则由x得 x-a由x得 x0,故()f x在(0,)单调递增.若 00得，无解.（3）当21xx即1k时，2()01xfxx故()fx的单调递增区间是(1,).（4）当21xx即01k（0k）时，由()0fx得，10kxk；由()0fx得，110kxxk或故()f x的单调递增区间是(1,0)和1(,)kk，单调递减区间是1(0,)kk.（5）当21xx即1k（0k）时，由

38、()0fx得，10kxk；由()0fx得，110kxxk或故()f x的单调递增区间是1(1,)kk和(0,)，单调递减区间是1(,0)kk.综上知:当0k时，()f x得单调递增区间是(1,0)，单调递减区间是(0,)；当1k时，()fx的单调递增区间是(1,)；当01k时，()f x的单调递增区间是(1,0)和1(,)kk，单调递减区间是1(0,)kk当1k时，()fx的单调递增区间是1(1,)kk和(0,)，单调递减区间是1(,0)kk.文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9

39、A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM

40、7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9

41、L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10

42、A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:

43、CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 H

44、I9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7文档编码:CM7Y5O4S3O6 HI9L6U4T2S9 ZG10A9A2R9R7

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