题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034001-28143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034001-14390.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034001-76015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034001-94071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034001-29665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-23239.png)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-29750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-97682.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-97477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034003-93758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034003-99833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034003-92397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034003-90156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034003-49286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034004-82798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-29750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034004-19507.png)
解析
试题分析:(Ⅰ)先求导,代入0可求得a的值。再将
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034004-74356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034004-60557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034004-74356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034005-39062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034005-39062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-23239.png)
试题解析:解:(Ⅰ)已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034001-28143.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034005-25016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034005-39172.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034001-14390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-97477.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034005-52310.png)
所以曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034001-29665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-23239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034003-93758.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034006-32127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034006-58860.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034006-68884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034006-80177.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034003-99833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034006-94910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-97682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-29750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-97682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034003-92397.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034003-90156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034007-80522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034007-31919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034007-68448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034007-48099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-29750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034007-80522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034007-68448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034008-50062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-97682.png)
上唯一极值点,所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034003-49286.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034004-82798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-97682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034008-72838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-97477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034008-24115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-29750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-97682.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034008-44133.png)
综上所述,当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034008-92503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-29750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034009-37354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034004-82798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034002-29750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034004-19507.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033950-85251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033951-61805.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033951-59236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033951-99685.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033951-99685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033951-58237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033952-36280.png)
(I)当a=2时,求f(x)的单调区间与极值;
(Ⅱ)若对于任意的x∈(0,+
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033944-13365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033926-39967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033926-86736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033926-99082.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033927-79243.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033927-15038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033927-48449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033917-56584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033917-95274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033917-48615.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033918-10682.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033918-36536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033918-10682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033858-82273.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033858-40799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033858-67680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033858-18053.png)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018033858-67680.png)
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