题目
题型:不详难度:来源:
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135421-17907.png)
(I)讨论
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135421-40494.png)
(II)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135422-68205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135422-39157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135422-29301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135422-50225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135423-89481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135423-13011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135423-68926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135423-39488.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135421-40494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135424-93611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135424-12369.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135424-36240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135424-82553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135425-84290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135425-84525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135425-78818.png)
此时函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135421-40494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135425-59490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135426-43401.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135426-39633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135426-49521.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135426-70306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135426-50905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135424-82553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135427-80628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135425-84290.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135427-37063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135425-78818.png)
此时函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135421-40494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135425-59490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135427-87960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135427-65203.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135428-75018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135428-10993.png)
此时函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135421-40494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135425-59490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135426-43401.png)
综上所述,当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135428-48093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135421-40494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135425-59490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135426-43401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135426-70306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135421-40494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135425-59490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135428-17217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135429-18900.png)
(II)由(I)可得当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135422-39157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135421-40494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135425-59490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135429-78588.png)
所以在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135429-75423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135429-48058.png)
由题意,对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135430-97890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135430-25648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135423-89481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135430-37540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135430-10901.png)
从而存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135430-84575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135423-89481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135430-37540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135431-67028.png)
即只需函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135431-94512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135430-84575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135423-89481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135430-37540.png)
又当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135431-86945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135431-93269.png)
所以在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135430-84575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135423-89481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135432-77065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135432-71235.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135432-77795.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135423-39488.png)
解析
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135412-88849.gif)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135412-14948.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135412-51571.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135413-63892.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135413-78517.gif)
(3)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135413-15320.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135413-78517.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135404-54580.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135404-41789.gif)
的图
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135405-94418.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135354-99237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135354-33323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135354-33323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135354-67278.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135344-16009.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018135337-44817.gif)
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