题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135306-28771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135306-48784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135307-35117.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135307-62243.png)
(2)若对于任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135307-52187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135307-17089.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135308-80888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135308-69303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135308-64638.png)
解析
试题分析:解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135309-57264.png)
因为函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135309-65689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135306-48784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135307-35117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135309-41530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135309-60372.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135309-50928.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135308-80888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135308-69303.png)
(2)由(1)可知,
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135310-31990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135310-35060.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135310-42203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135310-19082.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135311-85633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135311-87134.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135311-49722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135310-19082.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135306-48784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135309-65689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135311-31485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135311-76140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135312-79546.png)
则当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135312-17567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135309-65689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135312-79546.png)
因为对于任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135312-17567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135307-17089.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135312-29678.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135312-73758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135312-19659.png)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135313-76690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135308-64638.png)
点评:主要是根据导数的符号于函数单调性的关系来得到函数的极值和最值,得到求解,属于基础题。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135253-55203.png)
(I)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135253-67334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135253-90993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135253-19837.png)
(II)在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135254-46705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135254-71112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135254-94064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135254-91807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135245-79998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135245-14245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135246-30075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135236-56270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135236-85065.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135236-56270.png)
(2)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135236-18528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135236-58612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135236-56270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135236-54600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135237-75638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135237-41048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135226-50427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135226-55659.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135226-71314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135226-71970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135226-82179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135226-71970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135227-59284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135227-80799.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135155-19203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135155-25075.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135155-56443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135156-59620.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135156-30671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135156-70424.png)
(3)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135156-12126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135156-16017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017135157-67922.png)
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