题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035006-47724.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-56243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-66079.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-96471.png)
(Ⅲ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-50354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-54636.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-37619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-71421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-25887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-20277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-73619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-51867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-63812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-74128.png)
解析
试题分析:(Ⅰ)求出导数及切点,利用直线的点斜式方程即可得切线方程.
(Ⅱ)将
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-16428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-22153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-91827.png)
在本题中,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-30173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035009-97089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035009-81527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-71421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-25887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-20277.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-73619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-51867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-63812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-74128.png)
(Ⅲ)本题首先要考虑的是,所要证的不等式与函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035006-47724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035009-92117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035009-44098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035009-68362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035010-12611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035010-82403.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035010-96192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035010-66517.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035010-91930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035011-49274.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035011-44083.png)
与待证不等式比较,只要
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035011-80214.png)
试题解析:(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035011-86998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035012-90326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035012-46294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035012-83470.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035012-40680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035012-90931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035009-97089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035009-81527.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-71421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-25887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-20277.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-73619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-51867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-63812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035008-74128.png)
(Ⅲ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035013-21089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035013-12102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-56243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035013-16818.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035010-96192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035013-31366.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035010-91930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035011-49274.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035014-75722.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035011-80214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035014-58686.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035014-85179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035014-49850.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035014-65114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035015-97332.png)
所以:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018035007-54636.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034947-36692.png)
(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034947-83471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034947-92284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034948-38971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034948-27561.png)
(2)求证: 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034948-16959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034948-10309.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034948-69367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034949-94042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034949-85647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034949-21484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034928-18816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034929-70560.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034929-88373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034929-41400.png)
(2)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034929-31722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034930-85244.png)
(3)证明: 对一切
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034930-80597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034930-53861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034920-13635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034921-17975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034921-55658.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034909-33957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034909-68347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034909-25869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034909-25586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034909-70883.png)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034910-98946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034910-85031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034910-17007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034902-56286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018034902-77494.png)
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