题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044921-38127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044921-95554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044922-36647.png)
(Ⅰ)讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044922-69363.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044922-11070.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044922-31676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044923-34218.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044923-18569.png)
解析
试题分析:(Ⅰ) 利用导数分析单调性,注意分类讨论;(Ⅱ)利用导数分析单调性,进而求最值
试题解析:(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044922-69363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044923-17488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044923-97102.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044924-11525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044924-55020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044924-12970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044924-76271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044924-79245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044925-24829.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044922-69363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044925-27742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044925-39839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044925-96054.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044922-11070.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044925-98744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044926-32383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044922-69363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044923-17488.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044926-76307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044924-55020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044926-95052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044926-83058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044924-79245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044927-40760.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044922-69363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044927-70981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044927-14361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044927-85848.png)
(Ⅱ)证明:不等式等价于
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044927-77571.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044926-95052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044928-62511.png)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044928-31363.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044928-15699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044928-58066.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044929-58010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044926-95052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044929-75062.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044929-59136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044927-14361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044929-79687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044929-99281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044930-67706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044930-87175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044927-14361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044930-96384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044930-67706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044926-95052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044930-69232.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044913-67874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044902-12764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044902-26620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044903-87284.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044855-53871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044855-48417.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044855-14868.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044855-14868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044856-83249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044844-15316.png)
(1)若实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044844-33057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044844-74943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044844-39573.png)
(2)记函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044844-73982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044845-89136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044845-27667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044845-62696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044845-79331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044845-27667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044845-79331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044846-72161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044846-58598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044846-17218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044827-15990.png)
(1) 试讨论
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044828-76725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044828-36368.png)
(2) 令函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044828-69366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044828-39530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044829-41950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044829-99027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044829-25306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044829-68130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044830-84200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018044830-79620.png)
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