题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034324-61029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034324-86792.png)
(Ⅰ)当a=4时,求函数f(x)的单调区间;
(Ⅱ)求函数g(x)在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034324-71119.png)
(Ⅲ)若存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034325-29408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034325-59777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034325-78539.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034325-84127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034326-52727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034326-80281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034326-33125.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034326-64185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034326-83544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034327-49932.png)
解析
试题分析:(Ⅰ)求导数,根据
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034327-34408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034327-43214.png)
(Ⅱ)遵循“求导数,求驻点,讨论单调性,确定最值”.
(III) 由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034325-59777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034327-52465.png)
“分离参数”得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034328-93012.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034328-97189.png)
“表解法”往往直观易懂,避免出错.
试题解析:(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034328-76733.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034325-84127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034328-19934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034327-34408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034328-17349.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034325-84127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034326-52727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034326-80281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034326-33125.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034329-31482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034329-29284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034329-84691.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034329-15351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034330-53308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034329-29284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034330-16736.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034330-34765.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034330-53139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034330-71470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034331-90997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034330-16736.png)
在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034331-14169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034329-29284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034330-16736.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034326-64185.png)
(III) 由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034325-59777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034327-52465.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034328-93012.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034328-97189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034331-58262.png)
![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() |
![]() | 单调递减 | 极小值 | 单调递增 |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034333-94481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034334-80763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034334-49362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034334-37696.png)
∴实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034326-83544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034327-49932.png)
核心考点
试题【已知函数,(Ⅰ)当a=4时,求函数f(x)的单调区间;(Ⅱ)求函数g(x)在区间上的最小值;(Ⅲ)若存在,使方程成立,求实数a的取值范围(其中e=2.71828】;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/20191018/20191018034314-80623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034314-19323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034314-10945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034314-25553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034315-32645.png)
A.3 | B.![]() | C.2 | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034308-15975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034308-78192.png)
A.![]() | B.1 | C.![]() ![]() | D.![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034255-86220.png)
(Ⅰ)若曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034255-34367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034255-35022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034255-25144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034255-46004.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034255-66080.png)
(Ⅲ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034255-10279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034255-49901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034255-20067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034255-73537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034255-46004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034238-18076.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034238-65717.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034239-34485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034239-42724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034239-88387.png)
(Ⅲ)证明:当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034239-59144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034239-58737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034225-77992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034226-80083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034226-48239.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034226-46421.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034226-60778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034227-64653.png)
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