名校
解题方法
1 . 若函数
与函数
的图象存在公切线,则实数t的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1407269f353c9881c1eba58855b5d345.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c4473159277aed64ea96c4af087954.png)
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2024-01-18更新
|
1134次组卷
|
6卷引用:广东省广州市铁一中学2024届高三上学期第二次调研数学试题
广东省广州市铁一中学2024届高三上学期第二次调研数学试题(已下线)热点2-4 导数的切线问题(6题型+满分技巧+限时检测)(已下线)压轴小题11 函数的公切线问题(一题多变)重庆市南开中学校2023-2024学年高二上学期期末考试数学试题(已下线)高二期末模拟卷02(已下线)专题05导数的概念、导数计算及切线方程的9种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)
名校
2 . 已知函数
.
(1)若
在
处的切线
与直线
垂直,求
的方程;
(2)若
,且
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdb221b680754e21912398a4544b17ea.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d406340355cba74ae8a04702e7c3a48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/672b3ddf3bb965a8a946aec16d894dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-12-29更新
|
511次组卷
|
2卷引用:山东省泰安市新泰弘文中学2024届高三上学期第二次质量检测数学试题
名校
3 . 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)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
,
,令![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375188c08625c1198d55e189de16aa7e.png)
(1)当
时,求函数
在
处的切线方程;
(2)当a为正数且
时,
,求a的最小值;
(3)若
对一切
都成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c12b64c84b3bef41942a5a4f2409799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d89c293b2a43612f08d290746d0925a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375188c08625c1198d55e189de16aa7e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)当a为正数且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d967d4ec242cd32654fc5f96e72d5dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d94a7a0f5a35a8a19d3e003a7f58ba.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d70309304e6f4a34f8efa9b244a05de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8654e969a9b848729a9f2d4fee437606.png)
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2024-03-07更新
|
1731次组卷
|
13卷引用:上海市实验学校2022-2023学年高三下学期3月月考数学试题
上海市实验学校2022-2023学年高三下学期3月月考数学试题上海市同济大学第一附属中学2023届高三下学期5月月考(质控2)数学试题(已下线)模块八 专题11 以函数与导数为背景的压轴解答题上海市同济大学第一附属中学2023届高三三模数学试题上海市风华中学2024届高三上学期期中数学试题上海市浦东新区上海中学东校2024届高三上学期期中数学试题上海市上海师范大学附属中学2023-2024学年高三下学期3月月考数学试卷上海市育才中学2024届高三下学期第一次调研(3月)数学试题上海市青浦区2022-2023学年高二下学期期末数学试题(已下线)重难点04导数的应用六种解法(1)上海市浦东新区上海师大附中2024届高三下学期3月模拟考试数学试题上海市嘉定区育才中学2024届高三下学期(3月份)一调数学试卷江苏省无锡市江阴长泾中学2023-2024学年高二下学期3月阶段性检测数学试卷
解题方法
5 . 已知函数
,
的导函数为
.
(1)当
时,证明:曲线
与
轴相切;
(2)若不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11552225f4543675afce351ad4101997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a5f4dc2949e716cce475756d002da2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
6 . 设函数
,
.
(1)当
时,求函数
在
处的切线方程;
(2)讨论函数
的单调性;
(3)若
在R上恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c207efd83d75c1f69237d97616c726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)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/9b384412acba251d87902ab928902f16.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8559250e7a91f36fe7a8ec6ce6a1550f.png)
您最近一年使用:0次
2023-09-04更新
|
823次组卷
|
5卷引用:黑龙江省大庆市肇州县第二中学2023-2024学年高三上学期10月月考数学试题
黑龙江省大庆市肇州县第二中学2023-2024学年高三上学期10月月考数学试题(已下线)考点18 导数的应用--函数最值问题 2024届高考数学考点总动员【练】内蒙古呼和浩特市2024届高三第一次质量监测文科数学试题湖北省武汉市第七中学2023-2024学年高二下学期3月月考数学试卷安徽省马鞍山市第二中学2023-2024学年高二下学期阶段性检测数学试题
名校
7 . 已知函数
.
(1)求
在原点处的切线方程;
(2)当
时,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e05003d0c286bba55cd3760bcf41d2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b27038352779922e9dc2595bfaefb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fadae1ff01e9015d166ed46366ab6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
8 . 设函数
.
(1)若
,求曲线
在点
处的切线方程;
(2)若
,当
时,求证:
.
(3)若函数
在区间
上存在唯一零点,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ef7de45c7c920dff0762e81aaf70cf.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb9374a0245ffdcb4b23bd8bd5b662a.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
.
(1)若
,求
在
处的切线方程;
(2)若
对任意的
恒成立,求实数a的取值范围;
(3)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d801d630fad35839f90d61e46eba90f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](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/b6acb0f1ac694dd177e99fc385f23318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a09145206ea1060dbba927a9d12569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8324978292be369bed37401d013e121f.png)
您最近一年使用:0次
名校
解题方法
10 . 已知
,
,且
在点
处的切线与直线
垂直.
(1)求实数
的值.
(2)若
的图象经过原点,且
,当
时,
过点
的切线至少有
条,求实数
的取值范围.
(3)若
,且
,其中
,
均为正实数.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2dc19a078760863c7e681e59e0ec56b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8bb7e252de0e54ca82ad2c36ffba37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227d4946b9dbfdc8bef33b42b6a82572.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbab1a525c4451a43041defaa18a98f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9fab43d7bc79776880a47091152b46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa70fa7eb86c3733e2c1f1c7d07dd802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7892b90ae2ff71fd827c95e5aabc3049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca96bf407a3ba46ef3c59c5eee4137c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803b13fac1480b428cb4ee4555852024.png)
您最近一年使用:0次