1 . 已知函数
的导函数为
.
(1)若
,求曲线
在点
处的切线方程.
(2)若
存在两个不同的零点
,
(ⅰ)求实数
的取值范围;
(ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e15ecb3e777a4767f56bb7ceb105d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(ⅰ)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c701c5c07f7c584aadd218d9e341d3ac.png)
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解题方法
2 . 已知函数
.
(1)若
,判断
在
上的单调性,并用单调性的定义证明;
(2)设函数
,若对任意
,总有
,使得
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f44e619b41991f2002cc203be8d6f3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189b2da6c420bf8f8900002d14f65f72.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2773b25d35138dad01fadf8632f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d5a5e70f64f0933ae1e4ddec5fa2c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92a39100a738af90edc8da0fc3c5b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347ac85769012f89d1f9951684e1d7b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-02-21更新
|
453次组卷
|
2卷引用:海南省2023-2024学年高一上学期期末学业水平诊断数学试题(一)
3 . 若
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17738d3002af0ac440a7d99b6bb81174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b871cfc5927e45b7f0bc6f79b04610a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a689e013336266fa2c064ca4a8e3a1f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70d5254f252c669a6a10e12a10f35147.png)
(1)求
的单调区间;
(2)若函数
有两个不同的零点
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70d5254f252c669a6a10e12a10f35147.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45dd5f2ca27a25ef2d7e6d73834c3a17.png)
您最近一年使用:0次
5 . 若函数
有两个极值点,则实数
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f564e076026b644c47e843a08149887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
6 . 已知函数
.
(1)证明
;
(2)不等式
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350cfa662d2b23270307a1e149a56208.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8e8b6b50410876780b97fd192e8829.png)
(2)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e247f68b1f0c3e57c79176149871f512.png)
您最近一年使用:0次
解题方法
7 . 已知函数
.
(1)当
时,求
的单调区间;
(2)若对于任意的
(
为自然对数的底数),
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f945cce5d9ca4f54fecae6c67cab732.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039066d5102043c33f574103b0cf8233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
8 . 已知函数
.
(1)若
,求
的单调区间;
(2)若函数
有两个极值点
,
,且
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da86c33fca8699b4236f19a10de2f48.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf01377399cf983f9dd989a4ce6d2885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a1f09b2f92d21a568604e2143dad03.png)
您最近一年使用:0次
解题方法
9 . 已知函数
.
(1)若
在
上单调递增,求a的取值范围;
(2)当
时,设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570b6f9a08be03589c8ac5fc4e06d0b4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459d4fd718865a67559c3b6a179b8ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8152c197cf4b13a50e64b463401888.png)
您最近一年使用:0次
10 . 已知函数
,
.
(1)求曲线
在点
处的切线方程;
(2)若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2203e4a66767e7d68a0a54bfd7e034de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde0e1a00dff7250f5d109ef21813e32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次