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)
您最近一年使用:0次
解题方法
2 . 对于函数
,若在其定义域内存在实数
,
,使得
成立,则称
是“
跃点”函数,并称
是函数
的1个“
跃点”.
(1)求证:函数
在
上是“1跃点”函数;
(2)若函数
在
上存在2个“1跃点”,求实数
的取值范围;
(3)是否同时存在实数
和正整数
使得函数
在
上有2022个“
跃点”?若存在,请求出
和
满足的条件;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268a02d5d03acda37ffa689359bbf6c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/393f13ef0b9eb7794879ddc62b81808c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f107d30aa8a70a6f8af2f8982ba26a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/543945660885cd4c9ff3979e9358950e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)是否同时存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aede6e541ca96009882cb172a2796b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b9f2ab6b0423d25bc6a1a490f0d919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2022-02-18更新
|
656次组卷
|
2卷引用:江苏省徐州市2021-2022学年高一上学期期末数学试题