题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005028-67782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005028-82191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005028-43752.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005029-84144.png)
(2)用单调性的定义证明
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005029-84144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005028-82191.png)
(3)解不等式
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005029-72253.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005029-83090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005029-51486.png)
解析
试题分析::(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005030-57311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005030-18541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005029-83090.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005030-17361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005030-41135.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005030-17361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005030-94743.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005031-96061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005031-60158.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005029-84144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005028-82191.png)
(3)由题意知:
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005029-72253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005031-67162.png)
(2)知:
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005031-67162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005031-96786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005032-41206.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005032-99456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005032-51594.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005032-81453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005029-51486.png)
不等式解集为
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005029-51486.png)
点评:本题考查函数奇偶性与单调性的性质应用,着重考查学生对函数奇偶性的理、用定义证明单调性及解方程、解不等式组的能力,属于中档题。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005011-53658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005011-86548.png)
①对于任意的
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005011-94458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005011-25990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005012-77889.png)
③若
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005012-96441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005012-28826.png)
求
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005012-53570.png)
求
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005011-86548.png)
若对于任意
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005012-38909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005013-42066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205005013-61778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004928-58730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004928-18950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004929-99966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004929-43651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004929-93250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004929-50150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004929-73571.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004921-35362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004921-16947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004921-60857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004922-21015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004922-99340.png)
(1)若该公司的这种产品的年产量为
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004922-70337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004922-56469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004922-12282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004922-70337.png)
(2)当年产量为多少时,当年公司所获利润最大?
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004837-95914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004837-54829.png)
(1)判断函数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004837-49683.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004838-32250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004838-12549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004838-79883.png)
(3)是否存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004838-59190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004837-49683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004838-91855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004839-82496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004838-59190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004822-50517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004822-63669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004822-63289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004822-59073.png)
A.0 | B.![]() | C.1 | D.![]() |
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