题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060020-13537.gif)
(1)求证:函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060020-70063.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060020-87986.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060021-10111.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060021-99321.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060021-96350.gif)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060021-27636.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060021-99321.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060021-54240.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060022-69153.gif)
有无穷多个.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060022-61278.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060020-70063.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060020-87986.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060022-37423.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060020-70063.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060020-87986.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060023-77049.gif)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060023-85956.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060023-60807.gif)
(2) 令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060023-62997.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060023-18774.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060024-91766.gif)
………………………………………………………………6分
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060024-36416.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060024-42587.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060024-37691.gif)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060025-53782.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060025-96708.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060025-33142.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060025-62014.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060025-26025.gif)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060026-45861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060026-45355.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060026-45861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060026-89970.gif)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060026-59314.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060027-96362.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060026-45861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060027-38537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060026-45861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060027-62852.gif)
也不合题意; …………………………………………… 8分
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060027-66426.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060028-26523.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060027-38537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060028-62964.gif)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060026-45861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060027-38537.gif)
要使
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060028-65748.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060028-22874.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060028-80600.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060029-19989.gif)
综上可知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060021-96350.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060029-82028.gif)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060029-41879.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060029-47412.gif)
记
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060029-59077.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060030-27835.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060030-98220.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060027-38537.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060030-22074.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060030-36610.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060030-89986.gif)
所以在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060031-48491.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060031-69198.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060022-69153.gif)
解析
核心考点
试题【已知函数.(1)求证:函数在点处的切线恒过定点,并求出定点坐标;(2)若在区间上恒成立,求的取值范围;(3)当时,求证:在区间上,满足恒成立的函数有无穷多个.】;主要考察你对常见函数的导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060011-77378.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060012-29527.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060012-17477.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060012-56326.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060012-76095.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060013-55041.gif)
(3)若对
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060013-89481.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060013-71224.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060013-20021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060000-32242.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060000-94392.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060000-70654.gif)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060001-11930.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060001-31832.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060001-40123.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060001-72954.gif)
(Ⅱ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060001-34893.gif)
(Ⅲ)若存在x1,x2∈[﹣1,1],使得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060002-36992.gif)
注:e为自然对数的底数。
(本小题满分14分)
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055954-11805.gif)
(1)求实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055954-54140.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055955-41560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055955-23503.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055944-85075.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055944-19814.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055944-87443.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055945-15541.gif)
(2)对于数列
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055945-23320.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055945-87858.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055945-71725.gif)
① 证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055945-24745.gif)
② 考察关于正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055946-74933.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055946-83765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055946-78545.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055933-75110.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055933-54627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055933-10734.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055933-77666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055933-74621.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055934-90083.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055934-19056.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055934-49420.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055934-96574.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055933-77666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055933-74621.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055935-39258.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055935-18363.gif)
(2)函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055935-27524.gif)
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