题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035347-25661.png)
(I)当a=-l时,确定
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035347-81048.png)
(II)若f(x)在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-86220.png)
(Ⅲ)当a=-1时,证明
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-28798.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-46252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-59743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-25052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035349-37677.png)
解析
试题分析:(Ⅰ)通过求导数,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035349-27920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035349-88230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035350-34124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035350-72968.png)
(Ⅱ)遵循“求导数,求驻点,讨论区间导数值正负,确定端点函数值,比较大小”等步骤,得到
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035350-88911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035350-30461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035350-90248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035351-15111.png)
(Ⅲ) 根据函数结构特点,令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035351-97512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035351-97512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035351-75322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035351-91580.png)
试题解析:(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035351-43275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035352-95980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035352-48140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035352-25516.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035349-27920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035349-88230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-46252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-59743.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035350-34124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035350-72968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-46252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-25052.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-46252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-59743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-25052.png)
(Ⅱ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035352-42634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035350-30461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035352-25516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035349-88230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035352-62173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-46252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035352-62173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035353-49198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035353-13534.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035350-90248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035353-60289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035353-89013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-46252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035352-62173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035353-49198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035353-13534.png)
③若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035351-15111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035353-88931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035349-88230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-46252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035354-26097.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035354-14675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035350-72968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-46252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035354-69980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035354-12318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035355-33473.png)
综上
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035349-37677.png)
(Ⅲ) 由(Ⅰ)知,当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035351-43275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035348-46252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035355-16232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035355-62061.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035355-48525.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035351-97512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035355-43910.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035356-79981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035356-36756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035356-68034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035356-52950.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035357-25667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035357-88496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035356-68034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035357-43198.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035357-30779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035351-97512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035351-75322.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035351-91580.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035357-86008.png)
核心考点
试题【已知函数,其中实数a为常数.(I)当a=-l时,确定的单调区间:(II)若f(x)在区间(e为自然对数的底数)上的最大值为-3,求a的值;(Ⅲ)当a=-1时,证】;主要考察你对常见函数的导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035332-29351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035332-50304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035333-84936.jpg)
(Ⅰ)若曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035333-54174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035333-76326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035333-50557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035333-94957.png)
(Ⅱ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035333-54174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035334-92913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035333-94957.png)
(Ⅲ)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035334-13213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035334-10536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035317-60892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035317-97705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035318-94004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035318-29107.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035318-67724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035318-41586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035319-10254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035319-21143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035319-21143.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035319-85500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035319-92543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035319-92127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035320-42222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035308-44347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035308-65302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035308-18553.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035303-35480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035304-78335.png)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035304-72028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035304-74840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035304-85029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035304-44724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035250-38845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035251-55599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035251-83927.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035251-81837.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035251-10604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035251-46289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035252-83094.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035252-47757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035252-53367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035252-95920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035252-68645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035252-83094.png)
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