1 . 已知函数
,
.
(1)若
,求曲线
在
处的切线方程,
(2)当
时,试讨论函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a12f3130968876c5b5fd9ed21e5f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若
![](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/9b384412acba251d87902ab928902f16.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
名校
解题方法
2 . 记
,
为
的导函数.若对
,
,则称函数
为D上的“凸函数”.已知函数
,
.
(1)若函数
为
上的凸函数,求a的取值范围;
(2)若函数
在
上有极值,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4634d0714ad90046e2ec7f2305c4d16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1da2db85b44ae9ced8c09cd19593e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df0dd6144e9a30d1a063b690033c3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5329815595daacc8ac5177e263af0a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
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3 . 已知函数
.
(1)求函数
在点
处的切线方程;
(2)若对于任意
,都有
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/779050e4d0ddc1dbdd66631551295f5e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde0e1a00dff7250f5d109ef21813e32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-04-05更新
|
1259次组卷
|
4卷引用:广东省东莞市众美中学2023-2024学年高二下学期3月月考数学试卷
广东省东莞市众美中学2023-2024学年高二下学期3月月考数学试卷2024年河南省普通高中毕业班高考适应性测试数学试题(已下线)2023-2024学年高二下学期期中复习解答题压轴题十七大题型专练(1)(已下线)信息必刷卷02(北京专用)
名校
4 . 已知曲线
在点
处的切线的斜率为1.
(1)求实数a的值;
(2)求函数
的单调区间与极值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e104ab83409f86a65046c8f2ee8ad1dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(1)求实数a的值;
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2024-04-02更新
|
946次组卷
|
3卷引用:广东省东莞市常平中学2023-2024学年高二下学期3月阶段检测数学试题
广东省东莞市常平中学2023-2024学年高二下学期3月阶段检测数学试题(已下线)第二章导数及其应用章末综合检测卷(新题型)-【帮课堂】2023-2024学年高二数学同步学与练(北师大版2019选择性必修第二册)四川省成都市成都外国语学校2023-2024学年高二下学期4月期中考试数学试题
5 . 求下列函数的导数.
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb6590cdfebabb58791b75789998dd0.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfc436eb1738984ed3b50eca6569a02.png)
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c1d48956f4aa941769df888f7aeefa.png)
(4)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb6590cdfebabb58791b75789998dd0.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfc436eb1738984ed3b50eca6569a02.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c1d48956f4aa941769df888f7aeefa.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c0d2781306051c802c8f90eb0475db.png)
您最近一年使用:0次
2023-12-10更新
|
1824次组卷
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11卷引用:广东省东莞市众美中学2023-2024学年高二下学期3月月考数学试卷
广东省东莞市众美中学2023-2024学年高二下学期3月月考数学试卷陕西省延安市富县高级中学2021-2022学年高二上学期期末文科数学试题河南省周口市项城市第三高级中学2024届高三上学期第三次考试数学试题(已下线)专题02 导数的运算(十大考点)-【寒假自学课】2024年高二数学寒假提升学与练(人教A版2019)(已下线)专题10 导数12种常见考法归类(1)(已下线)专题1.2 导数的运算(七个重难点突破)-2023-2024学年高二数学下学期重难点突破及混淆易错规避(人教A版2019)(已下线)专题08 导数的运算 (六大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)(已下线)特训02 期末解答题汇编(第1-5章,精选38道)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)(已下线)6.1.3&6.1.4 基本初等函数的导数、求导法则及其应用(1)宁夏回族自治区吴忠市青铜峡市第一中学2023-2024学年高二下学期4月月考数学试题(已下线)5.2导数的运算——课堂例题
6 . 已知函数
.
(1)求函数
在
处的切线方程;
(2)若
是
的极值点,且方程
有3个不同的实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66aa600e8ebc54042affceac4efeaeb7.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31bc0c34811edba74dae3fcaed8f577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-07-08更新
|
577次组卷
|
3卷引用:广东省东莞市2022-2023学年高二下学期期末数学试题
7 . 已知函数
,
.
(1)讨论函数
的单调性;
(2)若
,且对任意
(其中
)都有
,求实数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83e99119d426e266f76b858b0bfb1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46844bfd93548d0f3e7338b02921849.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574c9d9c90d4ef56d665cf8413975c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a65cccb4906515dcf25d662176a86dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
22-23高二下·全国·课后作业
名校
8 . 求下列函数的导函数.
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb6590cdfebabb58791b75789998dd0.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4627d3ed2198808e6636bdf1d02d6a4.png)
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8bd6b0849515fc491605384b64506c.png)
(4)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc60ffe2943e125cdbec29fa482b237.png)
(5)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
(6)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb6590cdfebabb58791b75789998dd0.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4627d3ed2198808e6636bdf1d02d6a4.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8bd6b0849515fc491605384b64506c.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc60ffe2943e125cdbec29fa482b237.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
(6)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07793c3c0222de60cd9430689be9ce44.png)
您最近一年使用:0次
解题方法
9 . 求下列函数
的导数:
(1)①
;②
;
(2)若函数
在
处取得极值为7,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02bab662762deda1c820e1c0b44bf241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee6b979180912f9b8ff7c2fde4de7d3.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f61fba00150460184aac5f0ce1fc4fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次