题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-99309.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-78009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-49659.png)
(2)求证:在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140132-31911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-78009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140132-82295.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-78009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-49659.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140132-87923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140132-26202.png)
(2)要证明在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140132-31911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-78009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140132-82295.png)
解析
试题分析:解:(1)由已知
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140133-41167.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140133-55009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140133-78687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-78009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-49659.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-78009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-49659.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140133-33283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140133-14575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-78009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-49659.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140132-87923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140132-26202.png)
(2)证明:设
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140134-38881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140134-31052.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140134-50282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140134-18622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140135-47734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140132-31911.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140135-46920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140132-31911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140135-77205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140136-52765.png)
所以在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140132-31911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140131-78009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140132-82295.png)
点评:解决的关键是利用导数的符号判定函数单调性,并能结合极值得到最值,进而得到图象之间的关系,属于基础题。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140123-54566.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140124-47112.png)
A
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140124-89607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140124-71922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140124-15489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140124-93771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140116-98227.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140116-31997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140116-34900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140116-96899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140116-49963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140116-28648.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140101-18332.png)
(1) 求
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140101-57857.png)
(2)是否存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140101-59780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140101-88296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140101-94899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140101-36936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140101-59780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140054-32877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140055-43873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140055-66042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140054-32877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140055-66042.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140049-31830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140049-25041.png)
A.导函数![]() ![]() |
B.导函数![]() ![]() |
C.函数![]() ![]() |
D.函数![]() ![]() |
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