题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051303-82320.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-20918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-58474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-76824.png)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-43004.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-46061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-19532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-43004.png)
解析
试题分析:函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-43004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051305-16283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051305-59102.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-20918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051305-38083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051305-37425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051305-21399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051306-22291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-76824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051306-79502.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-46061.png)
(Ⅱ)由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051306-67054.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-19532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051306-25549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-43004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051305-16283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-43004.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051307-17942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051307-47757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051307-60828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051307-55733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051308-53988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051308-10177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051306-25549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051308-76662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051307-60828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051308-22991.png)
综上:当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-19532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051304-43004.png)
点评:中档题,本题较为典型,是导数应用的基本问题。曲线切线的斜率等于在切点处的导函数值。研究函数的极值遵循“求导数,求驻点,研究单调性,确定极值”。
核心考点
举一反三
(Ⅰ)当k=1时,求函数f(x)的单调区间;
(Ⅱ)当k∈(1/2,1]时,求函数f(x)在[0,k]上的最大值M.
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051237-43904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051237-21299.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051237-18411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051237-43515.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051237-43515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051237-89921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051237-48645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051237-21299.png)
(Ⅲ)对于
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051237-43515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051237-41262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051237-89408.png)
证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051237-18373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051225-53146.png)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051225-29106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051226-35775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051226-48729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051226-75011.png)
其中所有正确命题的序号为 .
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051211-95426.png)
(1)讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051211-52397.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051211-32052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051211-55992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051212-82279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051212-83993.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051212-48073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051212-28576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051212-40662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051158-25242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051159-92250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051159-63412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051159-76934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051159-56882.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051159-86423.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051159-19036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051159-56111.png)
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