题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130204-69129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130204-58275.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130204-90870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130204-17824.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130205-83855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130205-12667.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130205-41169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130205-84705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130205-16436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130204-17824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-25887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-98145.png)
解析
试题分析:若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130204-90870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130204-17824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130204-90870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-84336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130204-17824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130205-83855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130205-12667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130207-31926.png)
(1)函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-84336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130205-41169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130205-84705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130207-54790.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130207-34349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130205-16436.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130207-16604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130204-17824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130207-27346.png)
![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ↘ | ↘ | | ↗ |
故
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130204-17824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130208-12145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130210-57876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130209-33879.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130205-16436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130204-17824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-25887.png)
(2)结论:函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-98145.png)
证明过程如下:
由题意,函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130207-31926.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130210-33612.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-98145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130210-36748.png)
求导,得
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130210-40442.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130211-80684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130211-84490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130211-90196.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130207-16604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-98145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130211-78615.png)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ↗ | | ↘ | | ↗ |
故函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-98145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130213-32327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130212-53619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130213-61444.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130205-16436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-98145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130213-72152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130213-92613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-98145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130213-17033.png)
因为函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-98145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130212-53619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130213-72152.png)
所以对于任意
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130214-78588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130214-18501.png)
因为函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-98145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130213-32327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130213-72152.png)
所以对于任意
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130214-15178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130214-18501.png)
因为函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-98145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130213-61444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130214-62925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130214-40428.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-98145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130213-61444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130215-59968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130215-87274.png)
故函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130206-98145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130209-54095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130215-59968.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130200-48169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130200-48169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130200-59826.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130149-27211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130149-50547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130149-27211.png)
(1)求f(x)的解析式;
(2)是否存在正整数m,使得方程
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130149-82788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130149-35142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130141-40675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130141-17383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130141-26774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130142-90087.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130138-94891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130139-91248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130139-59997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130134-59465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819130134-37796.png)
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