解题方法
1 . 已知
.
(1)证明
在
处的切线恒过定点;
(2)若
有两个极值点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374d913147d7dc157a0bb67244f203a1.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
2 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb78f95705bf886cd6ecb60469e9a28.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4ec6c78bab05a5df3d9954a70846ec.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb45a2f8b4a14b62425a2561624e777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
您最近一年使用:0次
2019-12-27更新
|
1329次组卷
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8卷引用:2020届福建省仙游县枫亭中学高三上学期期末数学试题
2020届福建省仙游县枫亭中学高三上学期期末数学试题贵州省贵阳市普通高中2019-2020学年高三上学期期末监测考试数学(文)试题2020届河南省高三普通高等学校招生模拟考试理科数学试题黑龙江省哈尔滨市第九中学2019-2020学年高三上学期第一次月考数学文科试题(已下线)专题02 导数(文)第三篇-备战2020高考数学黄金30题系列之压轴题(新课标版)重庆市綦江中学2020-2021学年高二下学期第一次阶段性考试数学试题(已下线)专题02 导数(理)第三篇-备战2020高考数学黄金30题系列之压轴题(新课标版)四川省绵阳市南山中学实验学校2024届高三上学期“二诊”模拟数学(文)试题
3 . 已知函数
.
(1)当函数
与函数
图象的公切线l经过坐标原点时,求实数a的取值集合;
(2)证明:当
时,函数
有两个零点
,且满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75daba7fc442d8082bffb88cff1997b4.png)
(1)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914a49b0d7aedc593a3e87fbab7c31ca.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db0eb7b60e88da1d807797cb17f85d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4016b94dd9d9bf93f662e694214cf8b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0bd58cfff55ae4fd5ba9cc9a96c5b2.png)
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2020-07-05更新
|
4060次组卷
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7卷引用:福建省厦门双十中学2023届高三上学期期中考试数学试题
福建省厦门双十中学2023届高三上学期期中考试数学试题2020届江苏省苏州市高三上学期期末数学试题四川省绵阳南山中学2020届高三高考仿真模拟(一)数学(理)试题(已下线)专题21 函数与导数综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)(已下线)极值点偏移专题08极值点偏移的终极套路(已下线)卷20-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(北京专用)四川省泸州市泸县教育共同体2023届高三一诊模拟考试数学(理)试题
名校
4 . 已知函数
,曲线
在点
处的切线方程为y=2
(1)求a,b的值;
(2)当
且
时,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef7a69b6903ffc77b3979bd4c2c1ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(1)求a,b的值;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e30c903d8f8a05332af0b19e7e40df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda75174a7a2f1e32f7d476ebf293a89.png)
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5 . 已知函数
.
(1)当
时,求曲线
在
处的切线方程;
(2)讨论
的单调性;
(3)设
、
为曲线
上的任意两点,并且
,若
恒成立,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26b5bd951dfa97c79aa477529a49ae8a.png)
(1)当
![](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)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45dddee525114c09ee0d1205aed6e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3b54e0dcdc081d45fb3df933cddc29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8257e16ded4d6fb13308f02fd460371.png)
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6 . 已知函数
.
(1)求函数
在点
处的切线方程;
(2)若函数
只有一个极值点,求实数
的取值范围;
(3)若函数
(其中
)有两个极值点,分别为
,
,且
在区间
上恒成立,证明:不等式
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca47d2e8724200bf868215c66c5cfe40.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/903e63d4a34cc16c1f28b66298272889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d12d46d386c33dc0f9abcafb323c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db1b7b5e4953a249b88d2eec36364af.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/e2613fa3f3008e09c1204631b4b2c0d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694dc2a9102d1272d75be70a81bab75e.png)
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2020-01-12更新
|
505次组卷
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4卷引用:福建省建瓯市芝华中学2023届高三上学期暑期考试数学试题
名校
7 . 已知函数
在点
处的切线方程为
.
(1)求
的值;
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1ba8131458264562474856f4ccc4d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24f3197942ff7bd44f44651dd9123b2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90cb7da9501e3cc3a831f905d9d3750e.png)
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2019-05-18更新
|
973次组卷
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3卷引用:【市级联考】福建省福州市2019届高三第三次(5月)质量检测数学(文)试题
8 . 函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6a99faca87b50eb905f21c5fcdc8c4.png)
令
,
.
(1)求
并猜想
的表达式(不需要证明);
(2)
与
相切,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6a99faca87b50eb905f21c5fcdc8c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ef42799c2fa1e691a331b4d94fbc70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0e8e8f252eaa414599e70f147bad8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a4eff83c86011011a5e0e8b48ad5a8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c96bc7c7acf94b76def93c71dc156fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3dd436444caca45aa03d5332ff84f0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b56692fcfc67a9cac9e2ce34138ec6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2019-07-12更新
|
252次组卷
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2卷引用:福建省泉州市普通高中2018-2019学年高二下学期期末数学试题
名校
9 . 已知
是自然对数的底数,函数
与
的定义域都是
.
(1)求函数
在点
处的切线方程;
(2)求证:函数
只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cfb32405d71542f1c87dd58d9d5c4a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7b896474b95cf035d59530216139da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0324fecb070287715e3e8f2322056922.png)
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2019-04-13更新
|
710次组卷
|
2卷引用:【全国百强校】福建省厦门市厦门外国语学校2019届高三最后一模数学(文)试题
10 . 设函数
,曲线
在点
处的切线
与直线
垂直.
(1)求
的解析式;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee64ce1df4ae1e5baaded5f24e1ab1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f6ed76662695d4c711be57a16c3197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04836ba2906cf6f1e9aecd2a00824aae.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9393fc75283aabe25e4730e4aa04cad.png)
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