名校
解题方法
1 . 已知函数
在
是减函数.
(1)求实数a的取值范围;
(2)记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7bc56c99c9a6a751d92a8b398e82ee.png)
,当
时,
①求证:
在区间
内存在唯一极值点(记为
);
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5854a3e006a1503b38666e56381d91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
(1)求实数a的取值范围;
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7bc56c99c9a6a751d92a8b398e82ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5e07bf129b073f37b553fbca100172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91fdbfcf9ffd7cdf7a74a8680afea926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c642de19a879df2e18cc5c5c44bd5b07.png)
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2 . 已知函数
(
),
(
),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8799a2863f3c94175c23391cbaea519d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36183977fcdb1a87a5c7cef17133e6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() |
C.函数![]() ![]() |
D.过原点的动直线l与曲线![]() ![]() ![]() ![]() ![]() |
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2022-11-18更新
|
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4卷引用:江苏省镇江市句容碧桂园学校等四校2022-2023学年高三上学期12月教学情况调研数学试题
3 . 下列判断正确的有( )
A.当![]() ![]() |
B.当![]() ![]() |
C.![]() |
D.![]() |
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4 . 设函数
,
.
(1)若直线
是曲线
的一条切线,求
的值;
(2)证明:①当
时,
;
②
,
.(
是自然对数的底数,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0ec3c50f8ff3bbb30ba0a0962073f2.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87490be8d0cdb7bc6c39d1a37f3bc335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)证明:①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb31e419ea4e0ec8f06d8cb4e348debc.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4dacb2a0080a87354011933ee07008f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25da8298b6a96d627f3e8c990e55f0c.png)
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2022-09-19更新
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4卷引用:江苏省南通市2022-2023学年高三上学期第一次质量监测数学试题
2022·江苏南通·模拟预测
名校
解题方法
5 . 已知函数
.
(1)求f(x)的最大值;
(2)设实数m,n满足-1≤m<0<n≤1,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b942e34517f93047f314caa461fe307.png)
(1)求f(x)的最大值;
(2)设实数m,n满足-1≤m<0<n≤1,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1209a39f8f77893f07e9311143dbb51b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b74eea8629336d1b239515b0e6405d9.png)
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6 . 设函数
的导函数
存在两个零点
、
,当
变化时,记点
构成的曲线为
,点
构成的曲线为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab24f8e070f02389049f52089d6b29b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e557fedbb51d5a15e9774c7b94e9d45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27c0ab3e2d7698f082854bafe4174dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc47735cc385a3474bc1dabad322304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
A.曲线![]() ![]() |
B.曲线![]() ![]() |
C.对于任意的实数![]() ![]() ![]() |
D.存在实数![]() ![]() ![]() ![]() |
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2022-05-23更新
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5卷引用:江苏省苏州大学2022届高三下学期5月高考前指导数学试题
江苏省苏州大学2022届高三下学期5月高考前指导数学试题江苏省徐州市第七中学2022-2023学年高三上学期10月学情调研数学试题(已下线)专题08导数的概念、运算与几何意义-2022年新高三数学暑假自学课精讲精练(已下线)考向14 导数的概念及应用(重点)湖北省黄石市2023届高三下学期高考适应性训练数学试题
7 . 已知函数f(x)=
,下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/945a04d7ea457b458c7913942bc4ae33.png)
A.函数f(x)在(-1,0)上为减函数,在(0,+∞)上为增函数 |
B.当x1>x2>0时,![]() ![]() |
C.若方程f(|x|)=a有2个不相等的解,则a的取值范围为(0,+∞) |
D.(1+![]() ![]() |
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2021-08-13更新
|
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