题目
题型:解答题难度:简单来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043442-28204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-20354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-25577.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-57632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-79293.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-97051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-79293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043444-49548.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-57632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-79293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043444-75894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043444-20469.png)
解析
试题分析:(1)判断:若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-57632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-79293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043444-75894.png)
证明:当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-57632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043444-52566.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043444-75894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043444-76314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043445-79558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043445-63690.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043445-70731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-79293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043444-75894.png)
(注:用导数法证明或其它方法说明也同样给7分)
(2)因为
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-97051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043445-36684.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043445-44997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-79293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043445-32026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043446-50005.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043446-69133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-79293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043446-41383.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043446-77028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-79293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043446-51495.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043447-47746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043446-50005.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043447-85469.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043447-76281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043447-37477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043446-69133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-79293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043446-41383.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043447-14968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043448-35405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043448-35950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043443-79293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043448-74815.png)
综上得,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043444-20469.png)
点评:利用函数的单调性是解决函数最值及值域的最基本的方法,另外函数单调性的定义是证明单调性的最基本的方法,要掌握其步骤
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043435-94822.png)
⑴写出该函数的单调区间;
⑵若函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043436-43549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043436-34328.png)
⑶若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043436-45255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043436-49431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043436-22843.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043432-67373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043432-58680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043430-20818.png)
(1)求f(x)的单调区间;
(2)若当x∈[-2,2]时,不等式f(x)>m恒成立,求实数m的取值范围.
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043426-88998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043426-27928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043426-93408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043426-90907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043427-80939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043427-97987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043427-64470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043413-37211.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043413-69490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043413-78338.png)
(2)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043413-69490.png)
(3)若存在
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043413-86172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043413-51577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043414-87966.png)
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