名校
1 . 已知函数
和
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)求
在
处的切线方程;
(2)若当
时,
恒成立,求
的取值范围;
(3)若
与
有相同的最小值.
①求出
;
②证明:存在实数
,使得
和
共有三个不同的根
、
、
,且
、
、
依次成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d210070cc28a32cd9c3e848e195726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952a0cde9449eef7c5f11385c7432e71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b00d47ef1d331094530990ffe38e1d77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
①求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明:存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7aec235f9df6700f3cbc89c8bcecb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c8ad137a5bf6b24e0dd8dff417c31cc.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/d79fc0ce080b8ad8b63ba63259c680b6.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
您最近一年使用:0次
2023-01-10更新
|
900次组卷
|
3卷引用:天津市滨海新区塘沽第一中学2022-2023学年高三上学期期末数学试题
天津市滨海新区塘沽第一中学2022-2023学年高三上学期期末数学试题江苏省南京市宁海中学2022-2023学年高三下学期二月检测数学试题(已下线)江苏省南京市六校联合体2023-2024学年高三上学期11月期中数学试题变式题19-22
名校
解题方法
2 . 已知向量
满足
分别是线段
的中点,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/062c160660228a8636bf6ca10a71ad3e.png)
______ ;若点
为
上的动点,且
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/721efceb5495b22c8d3da8e0911eef86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ebc0ca5058cc10f21011114d11334aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481e426224c3a3ce9bb5a731eed81c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fc71e889289f1f4d126e9c2ab861f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/062c160660228a8636bf6ca10a71ad3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f2c98c84895030f3dffa92cb25ad20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/273b63fc788388fab8b4f685fdb83230.png)
您最近一年使用:0次
2022-12-09更新
|
511次组卷
|
2卷引用:天津市滨海新区塘沽第一中学2022-2023学年高三上学期第三次月考数学试题
名校
3 . 已知函数
,
.
(1)当
时,求函数
在点
处的切线;
(2)若
对任意的
恒成立,求实数
的取值范围;
(3)求证:
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1311c1c23e54391ff9052f0df09f485a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27bcb0a5f3d22e9df052879fb0d0d4d.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/7160d93f92089ef36f3dab809d3114b8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f822c5d0ca02fd710b9a35a3fc4c4374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/035638c27917660d1161757eb28a4015.png)
您最近一年使用:0次
2022-05-29更新
|
1483次组卷
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5卷引用:天津市滨海新区大港第三中学2022-2023学年高三上学期线上期末检测数学试题
名校
4 . 已知函数
,若函数
的零点有两个或三个,则实数
的取值范围为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9a4267cc335002cc9cfd81da33d64a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039f9392112593405d4c0f1bea7d31f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
5 . 已知函数
,
,若对任意的
存在
,使
,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8a7bce56d1f4a4763f814294a0bae9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570ee63283174fd04548771d0a97f7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87348f632b0064b0e305133c4e149f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea6e1bfbda5c4f6421ed18e802aba04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333d64bb394ff3b2d2baaed8542af1ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2022-05-26更新
|
844次组卷
|
4卷引用:天津市滨海新区塘沽第一中学2021-2022学年高二下学期期中数学试题
名校
解题方法
6 . 已知函数
.
(1)当
时,求曲线
在
处的切线方程;
(2)设函数
,若
在其定义域内恒成立,求实数
的最小值;
(3)若关于
的方程
恰有两个相异的实根
,求实数
的取值范围,并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3c1e888fee64604444c45c1e898576e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786d68c14cda1112feca467801ad35a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a2c01ac2a7f6ad7e03cb7a61daefab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bd18a3b1cd5d1f78bc787438c9cd9ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a3ad8c843c361565d0f3cb06da49f60.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
,
.
(1)当
时,求函数
在区间
的最大值和最小值;
(2)当
在
有解,求实数k的取值范围;
(3)当函数
有两个极值点
,
,且
时,是否存在实数m,总有
成立,若存在,求出实数m的取值范围,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d77f3bc7988706b2e78c4fe5899326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a89baf9991a0c6a88829651e798405.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e354f44c5841806fdc363073abdd052.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/250f52f9368f69cc259b345377cdf4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5775bb155af9aa79e36064f182aa1b16.png)
(3)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86135bd40536042536c1c7bed21d0171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040135d64192de075ba0cc9f11ddbc9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188979cabc18797286c36882c5c44551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba93f19e4328de1bad07d33c7d47cb95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03fac3149fc1cd8c3b65d0241527caae.png)
您最近一年使用:0次
8 . 已知函数
,
,若对
,
,
且
,使得
,则实数a的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97eddd7cb7976d72039ebd9471579f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd3826e263c0518b9628d3b20fcb0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0227652a12f07975989d7d87a5f60ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86363d44047e7a13439be95c5ada424f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a023c5493f5b5aef2b04c8ceee1f28db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/562346ba03ec1242636d78bc79e1368f.png)
您最近一年使用:0次
名校
9 . 函数
.
(1)试讨论函数
的极值点的个数;
(2)若
在定义域内恒成立,证明:
①
;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc79355151b8c468ee580ae5f90650cd.png)
(1)试讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85cfb467d32eb2176b97a626695c479.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec2dbe3f3bfcc85d7b44ac9e07e1f67.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef38b2a4a323405c551de2650850a868.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b7745dd967fac70fee753efed8c49aa.png)
您最近一年使用:0次
2021-09-17更新
|
611次组卷
|
3卷引用:天津市滨海新区汉沽第一中学2022届高三下学期第一次月考数学试题
名校
解题方法
10 . 已知函数
,
,则函数
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc0c68ab10a12bfa86d38f9fcb18bc3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.0 | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2021-08-16更新
|
925次组卷
|
5卷引用:天津市滨海新区塘沽第一中学2021-2022学年高二下学期第一次线上调研考试数学试题
天津市滨海新区塘沽第一中学2021-2022学年高二下学期第一次线上调研考试数学试题广西崇左高级中学2020-2021学年高二下学期第一次月考数学(文)试题黑龙江省哈尔滨市第一二二中学校2022-2023学年高二下学期4月月考数学试题(已下线)第13讲 导数的最值四种题型总结(1)(已下线)5.3.2函数的最大(小)值(第2课时)(分层作业)(4种题型)-【上好课】高二数学同步备课系列(人教A版2019选择性必修第二册)