题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033602-83196.png)
(1)证明函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033602-63064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-96378.png)
(2)若不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-82951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-79234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-23788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-92574.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033602-63064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-96378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-15485.png)
解析
试题分析:(1)对原函数进行求导,难易判断正负,再令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-23197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033604-11969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033604-31297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033604-26571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033604-26834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-96210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033602-63064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-96378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-95904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-32844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-59949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-13442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033606-16855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-59949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033606-62634.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033606-59981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033606-66765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-59949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033607-72878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033606-66765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-59949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033607-91468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033607-25856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-92574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-15485.png)
试题解析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033607-83365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-23197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033604-11969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033604-31297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033604-26571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033604-26834.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-96210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033602-63064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-96378.png)
(2)在原不等式两边取对数为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033607-76011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033608-49440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033608-69613.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-95904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033608-49951.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-32844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033608-41372.png)
由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-59949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-13442.png)
∴函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033606-16855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-59949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033606-62634.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033606-59981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033606-66765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-59949.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033607-72878.png)
∴函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033606-66765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033605-59949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033607-91468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033607-25856.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-92574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033603-15485.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033551-67605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033552-80218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033552-69585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033552-32481.png)
A.1 | B.2 | C.0 | D.0或2 |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033542-53350.png)
(Ⅰ)求证:函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033542-50153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033542-34763.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033542-28034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033535-91216.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033535-44736.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033535-56795.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033535-44736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033526-60386.png)
(Ⅰ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033526-36360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033526-20383.png)
(Ⅱ)如何上下平移
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033527-16618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033527-40895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033514-52267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033515-87184.png)
(Ⅰ)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033515-90076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033515-46756.png)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033515-90076.png)
(Ⅲ)若存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033515-86290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033516-27543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033516-55918.png)
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