题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042804-22944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042804-74837.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042804-51408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042804-76358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042804-33139.png)
(2)求函数的极大值和极小值,若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042804-68357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042805-93878.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042805-80603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042805-45490.png)
解析
试题分析:(1)本小题首先代入
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042805-21826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042805-80603.png)
(2)本小题首先求得原函数的导数,通过导数零点的分析得出原函数单调性,做成表格,求得函数的极大值
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042806-12447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042806-86922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042806-55360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042806-77125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042806-77125.png)
试题解析:(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042805-21826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042806-18664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042807-31796.png)
所以曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042807-63469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042807-43845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042807-86551.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042805-80603.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042807-55358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042808-18759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042808-96358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042808-80659.png)
因
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042808-72572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042809-43785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042809-11917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042807-55358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042809-79101.png)
x | ![]() | 0 | ![]() | ![]() | ![]() |
f’(x) | + | 0 | - | 0 | + |
f(x) | 递增 | 极大值 | 递减 | 极小值 | 递增 |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042806-12447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042806-86922.png)
若要
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042806-55360.png)
只需
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042806-77125.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042810-69104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042810-42536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042810-70993.png)
故所求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042805-93878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042805-45490.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042749-11422.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042750-61925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042750-87359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042750-18089.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042750-39426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042750-61925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042750-70342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042737-27481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042737-61581.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042737-97697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042737-11078.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042737-76424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042738-79646.png)
(3)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042738-36068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042738-26456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042738-92900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042739-42068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042739-50619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042732-90570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042732-24524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042732-57922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042732-88855.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042718-31836.png)
(I)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042719-27769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042719-26704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042719-26704.png)
(II)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042719-78970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042719-19384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042710-34055.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042710-55324.png)
A.![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.![]() |
D.![]() |
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