题目
题型:解答题难度:简单来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043454-85431.png)
(I)讨论
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043454-58520.png)
(II)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043454-58520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043454-70400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043455-67740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043455-85631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043455-19502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043455-90665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-47684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043455-90665.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-73615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-85430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-90577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-13976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-15398.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043457-41428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043457-37404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043457-73504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043457-97807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-88713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-97198.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-13976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-15398.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043454-58520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-57665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-11353.png)
(II)不存在
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043455-90665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-99352.png)
解析
试题分析:(I)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043454-58520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043459-81192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043459-51307.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043459-38983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043459-67972.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-73615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-85430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-90577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-13976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-15398.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043457-41428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043457-37404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043457-73504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043457-97807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-88713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-97198.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-13976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043456-15398.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043459-73719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043457-37404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043457-73504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043500-10523.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043500-10465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-97198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043500-33551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043500-15325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043500-85897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-97198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043454-58520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-57665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-11353.png)
(II)由(I)知,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043459-73719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043500-82071.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043501-75726.png)
又由(I)知,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043501-53637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043501-67703.png)
若存在
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043455-90665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-99352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043501-85229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043501-44302.png)
亦即
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043502-15388.png)
再由(I)知,函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043502-58844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-88713.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043502-29733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043502-95965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043503-62821.png)
故不存在
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043455-90665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043458-99352.png)
点评:典型题,本题属于导数应用中的基本问题,通过研究函数的单调性,明确了极值情况。通过研究函数的单调区间,得到直线斜率表达式。存在性问题,往往要假设存在,利用已知条件探求。本题涉及对数函数,要特别注意函数的定义域。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043449-88473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043449-83118.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043450-32012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043450-58806.png)
(Ⅱ)若不等式
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043450-66212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043450-31828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818043450-31677.png)
![](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)
![](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.
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