名校
1 . 已知函数
有最大值
,
(1)求实数
的值;
(2)若
与
有公切线
,求
的值.
(3)若有
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91c20849a830a86f287b7913a7b4652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845e5670761cc50147a6f50bc2a30b60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c939c087e55933859467ac8c5c57dfce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a18d6ca6f17a219faad5eebc5ec5f1.png)
(3)若有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b867c903bdbadb2f47301f64fa3213f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a18d6ca6f17a219faad5eebc5ec5f1.png)
您最近一年使用:0次
名校
2 . 已知函数
.
(1)求
的单调区间.
(2)若
存在两个不同的零点
且
.
求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74da4b06c434c46d5a8958ad77f2592.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de5655fa8e5b649a926b176942e856b.png)
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解题方法
3 . 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
|
510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
解题方法
4 . 已知函数
,设
为实数,若存在实数
,使
,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2d45dabdf607915cad3394f44496ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4d3d8363cd16978a4ef4fc06645a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
5 . 已知函数
,
.
(1)求函数
的极值;
(2)若存在
时,使
成立,求
的取值范围.
(3)若不等式
对任意
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1caffd948a4988649abd01b90909fb4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0d71d7a8aa3939e7d8827b3d22085a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd35f264952602c0e7a0e1495e42066a.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a87b990f23750af24468d551cc3e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b031ab4cf118d01042524d1e61d44378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
(3)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/600ab6c89658d28b6dab321288754fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67e753ca0eac59a7b2f4a2b78c0efd44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
您最近一年使用:0次
2022-10-26更新
|
791次组卷
|
3卷引用:天津市第四十七中学2022-2023学年高三上学期单元随堂测试数学试题
解题方法
6 . 设函数
,
.
(1)若曲线
在点
处的切线与直线
平行,求
的单调性和极小值(其中
为自然对数的底数);
(2)若对任意的
恒成立,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c73d95211fa6dc4e0a8f3225abc9ea1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0c3187c16fa72cdeb875a8a8e1711a.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f8368f7daaae96338581b7ad1e5d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81275801ac34e1c33ea8e6acccc18b28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4e4958ed58f1381277e35114d975bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff5a8f648d375cc6ccf6649cab698c6.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1def1bfcac87464ae8d938b4c7d16317.png)
您最近一年使用:0次
2022-10-23更新
|
330次组卷
|
2卷引用:天津市武清区杨村第三中学2022-2023学年高三上学期第一次过程性评价练习数学试题
解题方法
7 . 设函数
,
,其中
为实数.
(1)若
在
上是单调减函数,且
在
上有最小值,求
的取值范围;
(2)若
在
上是单调增函数,试求
的零点个数,并证明你的结论.
(3)若
有两个零点
,
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d6684ac4aae228409c7ec40e53c393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d02b502ebf8a79560b09101b29b8fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454a64eafc25db7f5b29afca3283d7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454a64eafc25db7f5b29afca3283d7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5388cf31728a7b14e9f69644363d42b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12a4eecd249473a831d0ee472470240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9565876bc50bceb63e5793c8c67a9032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64bf3ee83962aa5fb9f95ac27469bbb7.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
.
(1)若曲线
在
处的切线的方程为
,求实数
,
的值;
(2)当
时,
,且
,求证
.
(3)若
,对任意
,
,不等式
恒成立,求
的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d3b84631f2d689ddd86c869b75e0d82.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f8368f7daaae96338581b7ad1e5d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7152aea5d046953a8c931571be7c529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19033a637fa5bf046a6276fe76b71312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2fdeba282b028321696be7f90f2cbfe.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7b339246d52b29603d33c152f44de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01015e1339e400649049d5684852c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77e3de74f4c6064bfae2899a82033305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64bf3ee83962aa5fb9f95ac27469bbb7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e06d02e1cde6f8103d61f9a0c4717a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12a4eecd249473a831d0ee472470240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba20949b66d70ec7b20a4593f4711fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a025395568cfa5bb2890e085c0a574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
您最近一年使用:0次
2022-10-20更新
|
533次组卷
|
5卷引用:天津市新华中学2022-2023学年高三上学期月考(一)数学试题
名校
9 . 如图,点G为△ABC的重心,过点G的直线分别交直线AB,AC点D,E两点,
,
,则
=________ ;若
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd569ef9f9dfd0bfd989a7ea85cd2d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f85c32db8c9b9e974f606d7d326bbe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f537c893dfe2661ba4273cf218c72d34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b8168dfecf248c3d7b18bf63e0f6d6.png)
![](https://img.xkw.com/dksih/QBM/2022/9/14/3066409998417920/3067760863223808/STEM/3876e3d4ed5649f5b4794bebfca780d7.png?resizew=162)
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2022-09-16更新
|
568次组卷
|
2卷引用:天津市外国语大学附属外国语学校2022-2023学年高三上学期第一次月考数学试题
名校
10 . 已知函数
.
(1)当
时,求函数
的极值;
(2)若关于x的方程
在
无实数解,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3021befc8618d74375b2eadba940f07c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb95fe8ab68d221c70acdee5451cc73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
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2022-09-14更新
|
994次组卷
|
9卷引用:天津市南开中学2023届高三上学期统练2数学试题
天津市南开中学2023届高三上学期统练2数学试题四川省仁寿县文宫中学2022-2023学年高三9月月考数学(文)试题宁夏银川一中2023届高三上学期第二次月考数学(文)试题江西省上饶市第一中学2022届高三5月模拟考试数学(文)试题(已下线)专题10导数与函数的极值、最值-2022年新高三数学暑假自学课精讲精练黑龙江哈尔滨工业大学附属中学校 2021-2022学年高二下学期期末理科数学试题(已下线)第12节 导数的综合应用(已下线)4.3 利用导数求极值最值(精练)-【一隅三反】2023年高考数学一轮复习(提升版)(新高考地区专用)(已下线)第15讲:第三章 一元函数的导数及其应用(测)(基础卷)-2023年高考数学一轮复习讲练测(新教材新高考)