解题方法
1 . 已知函数
的定义域为
,若存在常数
,使得对
内的任意
,
,都有
,则称
是“
-利普希兹条件函数”.
(1)判断函数
,
是否为“2-利普希兹条件函数”,并说明理由;
(2)若函数
是“
-利普希兹条件函数”,求
的最小值;
(3)设
,若
是“2024-利普希兹条件函数”,且
的零点
也是
的零点,
. 证明:方程
在区间
上有解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa591ac00281f1eea7543a469fd427c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd8396d35da607e63ac84ea6421ba39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59f39674ae74c30b26cb76a61b22993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6342e0a5a8942cfb1cf535ceb2c50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d1bf1c6c43ac530314ddb800016149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56158cf62fb4fae6cc62a0c7ee460659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfedbf8e8ea4a9bdc4e67798b638b7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b9ad706062dd4e8d4f20e393c7dbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1695bdfdf958d0e11587c212a68a33c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61e05f651acdda29d79ccd63843f80e1.png)
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