题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065805-82669.gif)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065805-46817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065805-92319.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065806-45572.gif)
(2)求证:在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065806-97167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065805-46817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065806-45327.gif)
(3)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065806-94339.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065807-56962.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065807-59189.gif)
答案
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065807-56851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065807-97793.gif)
(3)证明见解析
解析
(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065807-74874.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065808-56673.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065808-47351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065808-92415.gif)
∴函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065805-46817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065805-92319.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065807-56851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065807-97793.gif)
(2)证明:令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065808-85954.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065809-34047.gif)
∵当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065809-64058.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065809-50254.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065809-21174.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065806-97167.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065809-51656.gif)
即在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065806-97167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065810-82184.gif)
∴在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065806-97167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065805-46817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065806-45327.gif)
(3)证明:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065808-56673.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065810-12434.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065810-29022.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065810-94604.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065810-72673.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065811-78664.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065811-96285.gif)
①+②得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065811-70089.gif)
≥
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065811-51938.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065812-39479.gif)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065810-29022.gif)
综上所述得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065806-94339.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065807-56962.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065807-59189.gif)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065751-50433.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065751-73189.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065751-23071.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065751-52124.gif)
(Ⅰ)函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065752-88202.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065752-93554.gif)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065752-16380.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065752-88202.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065752-88202.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065752-80503.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065746-57223.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065746-97196.gif)
A.在![]() | B.在![]() |
C.![]() ![]() | |
D.在![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065733-75914.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065733-61062.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065734-23268.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065734-26009.gif)
(Ⅰ) 求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065734-73529.gif)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065734-73529.gif)
(Ⅲ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065734-99316.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065735-83551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065735-96608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065735-96825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065720-12738.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065720-26935.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065720-32898.gif)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065720-43849.gif)
(Ⅱ)试证:对于区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065720-71324.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065720-83622.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065721-83194.gif)
(Ⅲ)若过点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065721-38686.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065721-37874.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065714-26608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018065715-12130.gif)
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