题目
题型:辽宁省期中题难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071246-24145.png)
(1)求函数f(x)的单调区间;
(2)设m>0,求f(x)在[m,m]上的最大值;
(3)试证明:对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071246-35230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071246-98180.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071246-12239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071246-76989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071246-87991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071246-86040.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071246-28366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071246-48326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071246-44959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071247-83043.png)
∴函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071247-46401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071247-49920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071247-72264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071247-81408.png)
∵当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071247-93286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071248-42016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071248-99725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071248-66774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071248-29234.png)
∴函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071248-29189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071249-36222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071249-35466.png)
(2)由(1)知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071249-56341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071249-65738.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071249-78530.png)
故①当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071250-80208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071250-57249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071250-65626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071250-73690.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071251-63891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071251-79771.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071251-98920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071251-62072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071251-82010.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071252-75909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071252-50064.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071252-68051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071252-94276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071253-88391.png)
(3)由(1)知当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071253-13010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071253-77319.png)
∴在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071253-34793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071253-52930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071254-49583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071254-16201.png)
∴对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071254-46217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071254-81600.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071254-15927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071255-12991.png)
即对
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071255-10835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071255-35116.png)
核心考点
试题【已知函数f(x)=-x(1)求函数f(x)的单调区间;(2)设m>0,求f(x)在[m,m]上的最大值;(3)试证明:对任意,不等式恒成立.】;主要考察你对函数极值与最值等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071236-63491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071236-64360.png)
(1)是否存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071236-61367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071236-86044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071236-37088.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071236-16529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071236-80910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071237-55028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071227-58061.png)
(1)某广告商要求包装盒侧面积S(cm2)最大,试问x应取何值?
(2)某厂商要求包装盒容积V(cm
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071227-38066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071228-15814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071216-50705.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071217-74419.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071217-81331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071217-17080.png)
(1)函数在闭区间
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071209-74306.png)
(2)函数在闭区间
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071209-38272.png)
(3)对于
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071209-36315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071210-49750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071210-44342.png)
(4)函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071210-72469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071210-35394.png)
其中正确命题的个数是
B. 1
C. 2
D. 3
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