题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130453-99578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130453-48462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130454-23042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130454-21803.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130454-21803.png)
(2)证明:当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130454-52616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130454-93707.png)
(3)证明:若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130455-16698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130455-65366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130455-94411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130455-61134.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130456-30919.png)
解析
试题分析:(1)根据导数的几何意义求方程;(2)构造新函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130456-65737.png)
试题解析:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130456-86865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130456-79598.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130453-48462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130454-23042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130457-28443.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130456-30919.png)
(2)令
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130457-82569.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130457-34906.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130457-22557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130458-32027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130458-82917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130458-28022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130458-71040.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130459-89330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130459-99644.png)
(3)先求
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130453-48462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130459-16943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130500-25931.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130453-48462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130459-16943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130500-37877.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130500-90527.png)
下面证明
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130500-67291.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130501-26317.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130501-80663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130501-66870.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130502-64780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130502-93706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130502-78674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130502-17396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130503-87413.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130500-67291.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130455-16698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130503-85372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130503-72762.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130503-81825.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130442-69897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130442-70345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130442-27418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130442-67351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130443-21653.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130435-15635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130435-71075.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130430-56620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130430-82201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130421-73085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130421-84754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130422-53647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130421-84754.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130415-12359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130415-66839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130415-77147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130415-94676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130416-36622.png)
(Ⅰ)求实数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130415-66839.png)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130415-77147.png)
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