题目
题型:解答题难度:简单来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054424-64473.png)
(Ⅰ)证明:函数f(x)在
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054425-54224.png)
(Ⅱ)是否存在负数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054425-84578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054425-63992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054425-84578.png)
答案
解:(1)任取
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054425-55514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054425-91154.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054426-82122.png)
∴函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054431-41523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054432-51844.png)
另解:如果应用导数证明请相应给分
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054432-74986.png)
(2)不存在 ……………………………………………………7分
假设存在负数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054432-10943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054432-55740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054432-19712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054433-36119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054433-13046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054433-85821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054433-82744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054433-61932.png)
所以不存在负数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054432-10943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054432-55740.png)
另解:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054433-12059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054434-18862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054434-90459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054434-24324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054434-24990.png)
所以不存在。
解析
核心考点
试题【(本小题满分12分)已知函数f(x)=;(Ⅰ)证明:函数f(x)在上为减函数;(Ⅱ)是否存在负数,使得成立,若存在求出;若不存在,请说明理由。】;主要考察你对函数的单调性与最值等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054419-88950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054419-96940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054420-95936.png)
(1)求证
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054420-30378.png)
(2)判断
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054420-70180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054419-96940.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054420-10757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054420-79404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054415-47544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054415-45384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054415-30868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054406-26974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054406-33492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054406-71493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054352-55402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054353-80004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054353-72550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054353-97105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054353-67493.png)
(I)讨论
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054353-15307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054354-69338.png)
(II)求
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054354-84017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054354-75258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054354-86295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054346-67782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054346-93439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818054346-49752.png)
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