1 . 已知函数
,若在区间
上存在
个不同的数
,使得
成立,则
的取值集合是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a77a88ce5c031298ba14cde733ac365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e1134b2b3376fd24db50d93096b2c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ae6558e11384a40f3a338b73385ee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb2aa63ea12351f82186b9d02b0af64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2 . 已知函数
.
(1)讨论
的单调性;
(2)若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e555d56535776367402baaad9fb457f.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
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解题方法
3 . 已知
.
(1)求曲线
在
处的切线方程;
(2)若对任意的
,且
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae26f39fa585d238261a54623b60e2b8.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd7af568e3d9f444beb0ff41426477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd0f3cae39f2f29b30ca47213cffdc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
4 . 已知
,
,若
和
是函数
的两个不同的极值点,则
的取值范围内的整数是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8090d2752e3330b66fffcd95694b0c0f.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/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfc8f775c0c874c4ea920136a91db8f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 已知关于x的实系数一元二次方程
有一对共轭虚根
,
.
(1)当
时,求共轭虚根
和
;
(2)若
,求实数a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3552a880182b6c7f54f320fe7483ace7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f498b6874410fb46e9807e04371e6e5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec9f93ddf1453ac95368dcc84e1e4342.png)
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解题方法
6 . 设
.
(1)若
,求函数
的图象在
处的切线方程;
(2)若
在
上恒成立,求实数
的取值范围;
(3)若函数
存在两个极值点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab44240a0cb09a1b9f5966c63fa290f3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae386699086599e0bcb0fbe59cffd9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd785bc48778543268feeca30728c34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca13a93b5f401c0d39ba52b0cffcb0.png)
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7 . 设函数
.
(1)若曲线
在点
处的切线方程是
,求a,b的值:
(2)求函数
的单调区间及极值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c382fadeb4696900e74b0c0624f0669.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd1dcfe0c394b37a58b20c3b8123d4e.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2卷引用:广东省广州市第十七中学2023-2024学年高二下学期期中考试数学试卷
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8 . 已知
,
,
,
,则下列大小关系正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678bc4e3642a01f2e6c3f82ae6af82b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503a28c3b4ee6e3894b28cc0c84deec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf9fbba9a4583674e07eaf65f4f0493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce59668a3be332c863098b978da5b85.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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457次组卷
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4卷引用:2024届河北省名校联盟高考三模数学试题
9 . 若曲线
有两条过坐标原点的切线,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb4a4cde325db98f123ffbbfd7ac623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 已知
,函数
,其中
.
(1)若
,
,写出函数
图像的一条水平切线的方程;
(2)若
,
,且满足
,证明:
;
(3)若存在
,使得函数
有唯一零点,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7569cd7e9b31ad838230133b9bc8314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34e050fbca6ba0d5390263131690a41.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7562f4853fe96f2054d3f03e4eb207b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73feb6b2d30ca5becd5711582d6ba008.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fcb5d3be7955ac79a959abad606a47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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