题目
题型:解答题难度:简单来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-20545.png)
(I)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-31645.png)
(II)对于函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-56308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-90095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-64483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-45258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-18674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-74423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180555-33479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-56308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-90095.png)
设函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180555-31554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180555-24470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180555-70057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-56308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-90095.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180555-63276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-31645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-56308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-90095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180556-57806.png)
解析
试题分析:(I)首先求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-31645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180556-17137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-31645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-31645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-31645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-56308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-90095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180556-80261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180556-65765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-56308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-90095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180557-20192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180557-90157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180557-54318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180557-53497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180556-57806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180557-61831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180558-91425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-56308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-90095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180556-57806.png)
试题解析:(I)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180558-73390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180558-50966.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180558-99684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180558-44503.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-31645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180559-67882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180559-41693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180559-40572.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180559-52721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180600-52238.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180555-63276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-31645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180600-62217.png)
(II)由(I)知
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180600-99029.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-56308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-90095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180556-80261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180556-65765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180600-42334.png)
设函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-56308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-90095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180557-20192.png)
应有
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180557-90157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180557-54318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180601-26701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180557-54318.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180601-44288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180557-53497.png)
则“分界线”的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180556-57806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180601-51008.png)
记
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180601-91124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180602-67768.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180602-72563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180602-15595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180602-37825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180559-67882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180559-41693.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180556-80261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180602-37825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180602-35839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180557-61831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180558-91425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180603-63402.png)
综上所述,函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180553-56308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180554-90095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180556-57806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180603-44962.png)
核心考点
试题【已知函数(I)求函数的极值;(II)对于函数和定义域内的任意实数,若存在常数,使得不等式和都成立,则称直线是函数和的“分界线”.设函数,,试问函数和是否存在“分】;主要考察你对指数函数图象及性质等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180543-85744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180543-46048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180544-31768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180544-39855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180544-23395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180544-53143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180544-78735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180545-59443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180544-23395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180545-49197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180545-69096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180545-90573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180545-25395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180546-83865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180546-83711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180546-54499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180546-67403.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180538-46500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180538-38812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180539-74726.png)
A.0 | B.38 | C.56 | D.112 |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180530-87160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180530-13198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180531-12436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180525-44913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180525-15027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180526-46038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180526-60874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180526-52186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180519-96964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180519-73607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180519-62918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180519-63789.png)
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