名校
1 . 已知函数
,关于
的不等式
的解集为
,其中
,
为常数.给出下列四个结论:
①直线
是曲线
的一条切线;
②
;
③当
时,
的取值范围是
;
④要使
取唯一的值,仅当
.
其中,所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe819909452c1edb8e1f0e3f1adc562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce84901e2f29f740265e278be8e34de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea69fb59dc615852a0d248675788d82e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a27c31d57a84a5928898de139cb40a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b5b0840d90d0654e9bcb0f866ff10d.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51969fc1a8030cef11cab59267689e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a50188f84f379b3d0418c54cbade7d7.png)
④要使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdc6e6a0e6584bea7deb91b0841fa28.png)
其中,所有正确结论的序号是
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名校
2 . 定义:若函数
图象上恰好存在相异的两点
满足曲线
在
和
处的切线重合,则称
为曲线
的“双重切点”,直线
为曲线
的“双重切线”.
(1)直线
是否为曲线
的“双重切线”,请说明理由;
(2)已知函数
求曲线
的“双重切线”的方程;
(3)已知函数
,直线
为曲线
的“双重切线”,记直线
的斜率所有可能的取值为
,若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ece491f9ba053a2ead5ad54138d779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d430e6eb5f8b43723db095937fbc74f7.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5776b27d76690a67770d954a47bfb0f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb6f04900fb8400a415b1067320a2f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e540ef465ca68c186cc972d54d3a268e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6b9ccddda8585a04f8ab4d4b4583a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a097fa8e3bfa45de1ea35f1ad907fe3.png)
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2024-04-17更新
|
1263次组卷
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6卷引用:辽宁省辽阳市2023-2024学年高三下学期二模数学试卷
辽宁省辽阳市2023-2024学年高三下学期二模数学试卷广西2024届高三4月模拟考试数学试卷河北省邢台市2024届高三下学期教学质量检测(一)数学试题(已下线)模块五 专题5 全真拔高模拟5(苏教版高二期中研习)(已下线)专题16 对数平均不等式及其应用【练】(已下线)拔高点突破05 函数与导数背景下的新定义压轴解答题(九大题型)
名校
解题方法
3 . 已知函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4a918bb38ac075acd36c60a7225499.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2023-07-31更新
|
368次组卷
|
7卷引用:辽宁省铁岭市清河高级中学2022-2023学年高二下学期3月月考数学试题
解题方法
4 . 已知函数
,
(1)若
,求
的图象在
处的切线方程;
(2)若
对任意的
恒成立,求整数a的最小值;
(3)求证
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9c594a89167c4dee4bc13e921a4799.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0511338aa078cca149b4eb2645e3a7.png)
(3)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968f8d63599c0206c0374006ba14c717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
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2023-07-14更新
|
489次组卷
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3卷引用:辽宁省朝阳市2022-2023学年高二下学期期末数学试题
5 . 已知函数
的图象与函数
的图象有且仅有两个不同的交点,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e05c465028a97e44f34b65e9258dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b907c64bce7b404b3bae277bb21d6a12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-05-29更新
|
1176次组卷
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6卷引用:辽宁省抚顺德才高级中学2023届高三硬核提分(二)数学试题
6 . 已知函数
,其中e是自然对数的底数.
(1)当
时,函数
的图象是否存在平行于x轴的切线,如果存在求出切线方程,如果不存在说明理由;
(2)当
时,若函数
在
恰有两个零点,求a的取值范围(参考:
,
;
,
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c6114ff97a454606c3c06d9f9aa271.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f23a1cabfd92862e151d26a1270af0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad3a3ed2f0ce23b00fe252d1a6c058b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c6c9579333fc6960cc209519c79759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/474a84b9005951d2efe7cd9a70d5e63e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c6c9579333fc6960cc209519c79759.png)
您最近一年使用:0次
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7 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
.( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f304a19256eb0935d95c2adc48eb4bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f57b5a7c0283d2638c7b5a0baba4040.png)
A.若曲线![]() ![]() ![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-04-30更新
|
1819次组卷
|
7卷引用:辽宁省沈阳市东北育才学校2022-2023学年高二下学期期中数学试题
名校
解题方法
8 . 已知函数
的图象在
处的切线方程为
.
(1)求
,
的值及
的单调区间.
(2)已知
,是否存在实数
,使得曲线
恒在直线
的上方?若存在,求出实数
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe57c09ce4f23c0ef11ad30da31d4c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af79f45b5880c72a349500da9d8e118d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ad3dcd5f916e1dfe8f2050d4dbebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-04-10更新
|
626次组卷
|
6卷引用:辽宁省抚顺德才高级中学2023届高三硬核提分(二)数学试题
名校
9 . 已知函数
,
.
(1)求
在
处的切线方程;
(2)判断函数
在区间
上零点的个数,并证明;
(3)函数
在区间
上的极值点从小到大分别为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbdd006d6c6aa4c00282f564718a03a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063fae1ac0d76584d4caf4a9c727a5b7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c1472000e0565b237baade33bf5a18.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad14579830d0293b1390911cb603eb02.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad14579830d0293b1390911cb603eb02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147f89995c5aa07ce7f797c308c9c7d2.png)
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2023-02-21更新
|
1217次组卷
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4卷引用:辽宁省鞍山市第一中学2024届高三第二次模拟考试数学试题
辽宁省鞍山市第一中学2024届高三第二次模拟考试数学试题北京市陈经纶中学2023届高三下学期综合练习一(开学考试)数学试题(已下线)第九章 导数与三角函数的联袂 专题四 利用导数证明含三角函数的不等式 微点3 利用导数证明含三角函数的不等式(三)天津市滨海新区塘沽第一中学2024届高三上学期第二次月考(期中)数学试题
名校
10 . 直线
、
为曲线
与
的两条公切线.
从左往右依次交
与
于A点、B点;
从左往右依次交
与
于C点、D点,且A点位于C点左侧,D点位于B点左侧.设坐标原点为O,
与
交于点P.则下列说法中正确的有( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6895afad6fca3165f077eb0176421109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cacaef9d61fb706067e893b9051fdc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26c23adc2a79b93771e113e0364e44fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4c7d5aee3615cdb65b3dd4e24da7bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2c2f3e635507d9fbe6323b1b6d4574.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4c7d5aee3615cdb65b3dd4e24da7bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-01-03更新
|
3472次组卷
|
4卷引用:辽宁省沈阳市东北育才学校2022-2023学年高三下学期高考适应性测试(三)数学试题
辽宁省沈阳市东北育才学校2022-2023学年高三下学期高考适应性测试(三)数学试题河北衡水中学2023届高三模拟数学试题(已下线)专题9 函数与导数 第3讲 导数的几何意义及简单应用(已下线)模块八 专题4 以导数为背景的压轴小题