题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024423-11150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-46733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-16778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-66168.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-18854.png)
(2)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-41592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024425-18526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024425-66224.png)
(3)设点C在函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024425-47179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024425-95262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024425-57702.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024426-37123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024426-73252.png)
解析
试题分析:(1)根据题意图象与
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-46733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-16778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-66168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024426-99165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024426-36204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024427-46753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024426-36204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024427-46753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-46733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-16778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-66168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024427-96843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024427-16143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024427-20158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024427-57117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024427-50542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024428-31595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024428-96327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024428-14088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024426-99165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024428-89870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024428-88079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024429-63042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024429-21107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024429-53575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024429-34253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024430-99642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024430-54726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024430-70987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024430-16421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024430-20894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024425-95262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024431-79841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024431-48013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024426-73252.png)
试题解析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024426-99165.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024426-36204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024431-29421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024425-66224.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024427-46753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024431-46066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024431-85193.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024432-24684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024432-93768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024425-66224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024432-22316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024431-29421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024425-66224.png)
于是当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024431-85193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024425-66224.png)
因为函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024423-11150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-46733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-16778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-66168.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024432-87936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024426-37123.png)
此时,存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024432-92934.png)
存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024433-48521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024433-34689.png)
又由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024425-66224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024433-89777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024433-54664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024426-37123.png)
(2)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024427-96843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024427-16143.png)
记
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024427-20158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024434-44848.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024428-31595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024434-46895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024434-95206.png)
则有
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024434-66443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024434-43222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024428-14088.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024426-99165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024428-89870.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024424-41592.png)
(3)依题意有
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024428-88079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024429-63042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024429-21107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024429-53575.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024435-99295.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024429-34253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024430-99642.png)
由直角三角形斜边的中线性质,可知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024430-54726.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024430-70987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024430-16421.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024435-56314.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024435-31302.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024435-62338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024430-20894.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024425-95262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024431-79841.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024431-48013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024426-73252.png)
核心考点
试题【设函数,其图象与轴交于,两点,且x1<x2.(1)求的取值范围;(2)证明:(为函数的导函数);(3)设点C在函数的图象上,且△ABC为等腰直角三角形,记,求的】;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/20191018/20191018024413-14764.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024414-71013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024414-87846.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024414-87846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024414-10331.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024414-71013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024414-28374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024414-23942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024358-57735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024358-10806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024358-17698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024358-37647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024358-82594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024359-83085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024359-27116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024359-27993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024359-40238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024400-87029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024400-89567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024400-73615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024400-52818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024400-65676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024346-16805.png)
⑴求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024346-76615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024346-66417.png)
⑵当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024346-62644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024346-15466.png)
⑶若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024347-16089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024347-30754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024347-31605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024337-84240.png)
⑴求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024338-91060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024338-96896.png)
⑵若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024338-44274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024338-86031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024330-60632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024330-66221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024330-67247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018024331-50835.png)
A B C D
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