题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-11347.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-43462.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-48614.gif)
(Ⅰ) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-35309.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-45306.gif)
(Ⅱ) 若不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064141-65638.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064141-84868.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-48614.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-45306.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064141-95034.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064141-29746.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-45306.gif)
(Ⅱ)a的取值范围:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064142-39238.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-45306.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064142-75175.gif)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-35309.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064142-72453.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064142-64495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064143-52000.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064143-91866.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064143-49951.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064143-32447.gif)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-45306.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064141-95034.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064141-29746.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-45306.gif)
(Ⅱ) 令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064143-51488.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064144-14572.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064144-53843.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064144-16919.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-43462.gif)
x | ![]() | ![]() | ![]() | 1 | ![]() |
![]() | + | 0 | - | 0 | + |
![]() | ![]() | 极大值 | ![]() | 极小值 | ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064145-59347.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064146-80592.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064146-52755.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064140-45306.gif)
对于
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064146-50753.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064144-16919.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064146-11242.gif)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064141-84868.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064147-54102.gif)
由题意,不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064141-65638.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064141-84868.gif)
所以得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064147-84216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064142-39238.gif)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064129-39076.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064129-85732.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064129-30325.gif)
(2)求证:不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064129-69196.gif)
(3)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064130-16336.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064116-79048.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064116-98860.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064116-92693.gif)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064116-48749.gif)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064116-49232.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064116-77566.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064117-47116.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064117-37544.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064117-26435.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064106-43491.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064100-65533.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064101-96371.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064101-32792.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064056-44384.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064056-64872.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018064057-41307.gif)
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