题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150603-30512.gif)
(1)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150603-13441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150604-55345.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150604-81008.gif)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150604-40711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150603-13441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150604-28850.gif)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150604-40711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150604-39482.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150605-79145.gif)
答案
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150605-25970.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150603-13441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150605-75200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150606-24664.gif)
(3)l略
解析
(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150603-30512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150606-55171.gif)
∵ 函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150603-13441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150606-33667.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150606-74478.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150607-28766.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150607-41778.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150607-28766.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150607-83901.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150607-28766.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150605-25970.gif)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150604-40711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150607-78334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150608-32014.gif)
∴ 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150608-92385.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150608-55246.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150603-13441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150608-92385.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150608-82691.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150609-55958.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150603-13441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150608-82691.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150603-13441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150605-75200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150609-77170.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150609-68298.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150610-88281.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150610-39879.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150610-56758.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150603-13441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150605-75200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150606-24664.gif)
综上可知,函
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150610-72282.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150603-13441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150605-75200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150611-16441.gif)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150604-40711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150611-26752.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150607-78334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150603-13441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150606-33667.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150611-92794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150611-19883.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150612-72098.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150612-73803.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150612-50594.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150612-90949.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150612-13286.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150613-29740.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150613-16919.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150613-78486.gif)
即对大于1的任意正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150613-44404.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150613-78486.gif)
核心考点
试题【(本小题满分15分)已知函数(1)若函数在上为增函数,求正实数的取值范围;(2)当时,求在上的最大值和最小值;(3)当时,求证:对大于1的任意正整数,都有】;主要考察你对函数的单调性与导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150335-22976.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150335-44026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150335-16862.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150335-16862.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150335-44026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150335-22976.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150335-44026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150335-93495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150336-43945.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150335-44026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150335-22976.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150335-44026.gif)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150336-84063.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150336-33641.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150336-59854.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150336-26421.gif)
以上四个函数在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150337-82993.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150337-65855.gif)
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150224-10809.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150224-82034.gif)
(1)用实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150225-80780.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150225-60862.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150225-80780.gif)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150225-13452.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150225-44151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150225-15053.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150225-80780.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150226-66967.gif)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150226-76905.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150226-55890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150226-84204.gif)
求证:必存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150227-49013.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150227-51151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150309-64966.gif)
A
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150309-20470.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150309-94016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150304-98539.jpg)
A (-∞,)∪(,2) B (-∞,)∪(2,+∞)
C (-1,0)∪(1,3) D (-∞,0)∪(,2)
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150153-65818.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150153-53155.gif)
(1)若a=1,求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150154-34660.gif)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150154-34660.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150154-74541.gif)
(3)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150154-70911.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150154-21094.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150155-78358.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018150154-74541.gif)
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