题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195755-70326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195756-46566.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195756-51882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195757-58664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195757-25250.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195757-91616.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195756-51882.png)
(III)当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195757-76990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195758-78661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195758-34701.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195758-63058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195758-78306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195758-76560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195759-40282.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195759-75877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195759-15887.png)
解析
试题分析:(Ⅰ)令
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195800-79366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195800-51224.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195800-27422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195801-40248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195801-49001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195801-63346.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195758-63058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195758-78306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195758-76560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195759-40282.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195801-14609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195802-45476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195802-62793.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195802-75531.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195803-60878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195803-16630.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195759-75877.png)
(III)当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195757-76990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195803-14153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195803-97047.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195804-84561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195804-35980.png)
首先证明
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195804-67373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195804-31128.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195805-77863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195805-26038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195805-46378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195804-31128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195806-69479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195804-67373.png)
由(Ⅰ)可知
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195806-93029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195759-15887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195806-25039.png)
综上
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195759-15887.png)
点评:难题,不等式恒成立问题,常常转化成求函数的最值问题。不等式恒成立问题,往往要通过构造函数,研究函数的单调性、极值(最值),进一步确定得到参数的范围。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195713-69562.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195713-18253.png)
(Ⅱ)若存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195713-25451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195714-28506.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195714-35693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195601-62261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195601-15211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195602-32164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195555-77988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195535-16024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195535-16024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195535-16024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195536-73574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195525-45246.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204195525-78676.png)
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