题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050923-85307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050923-35652.png)
(Ⅰ) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-93733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-84174.png)
(Ⅱ) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-32637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-84174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-98543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-50650.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-84174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-99523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-15102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-47343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050925-66390.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-93733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050925-72278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050925-86140.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050925-58711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050925-67803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050925-91894.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050925-35194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050925-92151.png)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | 极大值 | ![]() | 极小值 | ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-84174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-99523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-15102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-47343.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050926-28292.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050925-58711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050925-67803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050926-73518.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050926-89672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050926-69073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050926-96551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050927-45963.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050927-22926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050927-81858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050927-71615.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050927-16659.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050927-66033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050927-94253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050927-15203.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050928-16683.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050928-93776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050928-20305.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050928-54026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050928-60166.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050928-82583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050927-45963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050928-40167.png)
所以存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050928-18878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050928-50387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050929-32062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050929-44073.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050929-42538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050929-84211.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050928-82583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050929-44507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050930-35785.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050930-99350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050930-84196.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050930-57030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050927-45963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-93733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050930-27642.png)
综上,函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-84174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050924-98543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050925-66390.png)
(1)根据k的取值化简函数的表达式,明确函数的定义域,然后利用求导研究函数的单调区间,中规中矩;(2)借助构造函数的技巧进行求解,如构造
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050931-57714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050931-46703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050928-93776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050930-57030.png)
【考点定位】本题考查函数的单调性和函数的最值问题,考查学生的分类讨论思想和构造函数的解题能力.
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050900-44372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050900-40906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050900-97398.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050900-39673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050900-73927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050900-17560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050900-73927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050900-97398.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050900-17560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050900-30951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050900-39673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050842-27207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050842-25489.png)
(1) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050842-45899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050842-92854.png)
(2) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050842-39761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050842-92854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050843-73540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050843-54199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050843-52600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050833-38025.png)
(II)若不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050834-40480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050823-67672.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050823-79261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050823-62569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050823-59714.png)
(Ⅱ)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050823-23788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050823-21101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050824-21993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050811-68562.png)
(I)求f(x)的极小值和极大值;
(II)当曲线y = f(x)的切线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050812-76027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050812-76027.png)
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