名校
1 . 已知函数
.
(1)讨论
的单调性;
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26b060a1a793fa7d536d5e733e5f82d9.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf1b1edc850b3a0aca5796830a6ce261.png)
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解题方法
2 . (1)证明:当
时,
;
(2)已知函数
,若
是
的极小值点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2acbfad5866c69207ec8ca7f39fe7c7d.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0172d1295992e244650b29b964afc052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)当
时,证明:
.
(2)若函数
,试问:函数
是否存在极小值?若存在,求出极小值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/101e3891ef8ae75f240e6081b9d0dc81.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b12f2ff24c52fded1dfd0f0b6940a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f88baa414c8b4a16a46234b7b1d874d.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d85caf6029742b5c99994233f76e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
.
(1)若函数
在
上是增函数,求正实数
的取值范围;
(2)当
时,求函数
在
上的最大值和最小值;
(3)当
时,对任意的正整数
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac15cac5b3af917dfc947318d968121.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b448fe164c2c2931805e3b3847dcdd75.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f5e5ba3a62f61ff22319d3decfdc48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742254b2bd8972eb9d52341ed2ef98f7.png)
您最近一年使用:0次
名校
5 . 已知函数
,其中
.
(1)讨论
的单调性;
(2)若
有两个极值点
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1009335ff006785dc8acaf2b955f34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de11c4103b6b4f702ff0728f2a6161fe.png)
您最近一年使用:0次
名校
6 . 已知
.
(1)求
极小值点的最大值;
(2)证明:当
时,
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa98d01d1a048092f8807da9c036376.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80a0c3b1c8baa969ab154985e56ffc16.png)
您最近一年使用:0次
名校
7 . 关于函数
,下列判断正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d42bc1614c3372edf362b4c07154fba.png)
A.![]() ![]() |
B.函数![]() |
C.存在正实数![]() ![]() |
D.对任意两个正实数![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-04-04更新
|
387次组卷
|
3卷引用:山东省烟台第一中学2023-2024学年高三上学期12月份月考数学试题
名校
8 . 已知函数
,(
为自然对数的底数).
(1)求曲线
在
处的切线方程
(2)若不等式
对任意
恒成立,求实数
的最大值;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8294bb352cef50b3a8961fcf0474aa6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e69e0bad37111c1169746941ac1f833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f47dd5fc03cf0d593fcf67b5d18d1c2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f2416d1f75a45a314331146550832e.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bac345bdfae4f716fde3946ed3708c2.png)
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解题方法
9 . 已知函数
,
.
(1)当
,
时,证明:当
时,
恒成立;
(2)当
时,若函数
在
处取得极大值,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304ae19859127998c3bc262d7b2b70e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681d6d27b23b1c41834d7516122f73f9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f043567da9d56738141114eb678706bf.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3f749686fc3926d7ca6c09ee6b4aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1bf5207dc0a8840f3a7188ee29d0d9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
您最近一年使用:0次
解题方法
10 . 已知函数,
.
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1613d377a07850c72cbec354b7a3000f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eebeb0c65327c1472d14023a5027778.png)
您最近一年使用:0次