题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053910-77796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053910-88855.png)
(I)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053910-85713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053910-63561.png)
(II)若对任意
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053911-17268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053911-85615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053911-10459.png)
(Ⅲ)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053911-13020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053911-77417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053912-87044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053912-93335.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053910-85713.png)
(法一)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053912-27867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053910-63561.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053912-18108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053912-27101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053912-82933.png)
(法二)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053913-68998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053913-64393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053913-84440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053913-92786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053913-77107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053912-27101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053912-82933.png)
(2)由题意知,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053911-85615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053914-25620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053914-69354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053914-92223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053914-24704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053914-71561.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053915-97616.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053915-46501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053915-49862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053915-69892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053915-21409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053914-71561.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053916-29541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053916-47688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053916-10265.png)
(可用导数方法证明单调性:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053916-15255.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053916-11250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053914-25620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053917-17534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053914-25620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053916-11250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053914-25620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053917-90870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053917-17534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053914-25620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053917-11709.png)
所以实数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053911-10459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053917-20554.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053917-68288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053918-88754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053918-13890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053918-86155.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053918-96863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053918-30992.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053918-69089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053919-65861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053919-85386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053919-53529.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053919-58648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053919-62493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053920-69150.png)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053920-28002.png)
综上所述,当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053919-65861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053920-54716.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053919-62493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053920-83854.png)
解析
核心考点
试题【已知函数;.(I)当时,求函数f(x)在上的值域;(II)若对任意,总有成立,求实数的取值范围;(Ⅲ)若(为常数),且对任意,总有成立,求M的取值范围.】;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/20190818/20190818053907-36708.png)
A.R + | B.{y|y≤1} | C.{y|y≥1} | D.{y|0<y≤1} |
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053904-35514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053854-27703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053854-20320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053854-70991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053854-26736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053855-33673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053855-30646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053855-80675.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053850-60397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053850-50290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053851-93198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053851-89586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053851-26793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053845-27902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053845-45670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818053846-42084.png)
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