题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055222-94192.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055222-84614.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055222-91860.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055222-99030.gif)
(1)试确定
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055223-76682.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055223-32638.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055222-84614.gif)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055223-78775.gif)
(3)求证:对于任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055223-29615.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055224-53104.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055224-80946.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055224-48380.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055224-20113.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055224-94287.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055225-18802.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055223-32638.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055225-41507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055225-55156.gif)
欲
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055223-32638.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055222-84614.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055225-32162.gif)
(2)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055223-32638.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055225-41507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055225-55156.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055223-32638.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055226-88017.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055226-74677.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055226-55650.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055223-32638.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055226-67230.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055226-19741.gif)
从而当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055222-91860.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055227-50304.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055227-88880.gif)
(3)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055227-37417.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055224-80946.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055227-66613.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055227-55245.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055227-55245.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055228-49315.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055228-66529.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055228-51776.gif)
所以 ① 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055228-46540.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055229-60721.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055229-36390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055228-49315.gif)
② 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055229-38401.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055229-59752.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055229-13072.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055229-36390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055228-49315.gif)
③ 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055230-61040.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055230-38528.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055229-36390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055228-49315.gif)
④ 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055230-32688.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055229-36390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055230-14144.gif)
综上所述, 对于任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055223-29615.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055224-53104.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055224-80946.gif)
且当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055230-19474.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055231-71069.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055229-38401.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055231-71069.gif)
解析
核心考点
试题【已知函数定义域为(),设.(1)试确定的取值范围,使得函数在上为单调函数;(2)求证:;(3)求证:对于任意的,总存在,满足,并确定这样的的个数.】;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/20191018/20191018055213-17208.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055213-19280.gif)
(Ⅰ) 求实数a的取值范围;
(Ⅱ) 若x1∈(0,1),x2∈(1,+
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055213-17451.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055213-19280.gif)
注:e是自然对数的底数.
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055201-24039.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055201-34527.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055201-58515.gif)
(2)若对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055201-95998.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055201-47498.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-37334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-96510.gif)
(1) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-69339.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-70706.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-45601.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-80132.gif)
(2) 证明: 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-14653.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055147-34429.gif)
(3) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055147-44853.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055147-83488.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055147-93663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055147-86717.gif)
已知定义在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055132-76741.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055133-86170.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055133-26312.gif)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055133-94042.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055133-76578.gif)
求证:当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055133-13391.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055134-88929.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055134-30169.gif)
(Ⅱ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055134-77526.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055134-73182.gif)
求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055133-26312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055123-88595.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055123-30634.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055123-30634.gif)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055123-23045.gif)
(Ⅲ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055123-80041.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055124-87782.gif)
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