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1 . 已知函数
.
(1)证明函数
的图象过定点;
(2)设
,且
,讨论函数
在
上的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84117b58944d6788691c2b24c070bb47.png)
(1)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71badab736269c6567a3977823e2f9b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3387f999c9cba4a1a083959709371447.png)
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2024-02-03更新
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382次组卷
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4卷引用:重庆市2023-2024学年高一上学期期末联合检测数学试卷
重庆市2023-2024学年高一上学期期末联合检测数学试卷重庆市2023-2024学年高一上学期期末数学试题福建省厦门市第一中学2023-2024学年高一上学期期末模拟数学试题(已下线)4.4.2对数函数的图象与性质(第3课时)
2023·上海·模拟预测
名校
2 . 已知
.记
,其中常数m,
.
(1)证明:对任意m,
,曲线
过定点;
(2)证明:对任意s,
,
;
(3)若对一切
和一切使得
的函数
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df569b67897be7670d10c7b7d06af16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e2696b1a336d7ab14b50d6ca80be95a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)证明:对任意m,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)证明:对任意s,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6819945aa00328aa3073e581cdfd39.png)
(3)若对一切
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed57d79c717fc8cf7ede3d9995c98359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4ff4809078ded17cd2674176342d6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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