名校
1 . 已知函数
.
(1)证明函数
有唯一极小值点;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546ae928f16d456f73c46dcd5e58d9bb.png)
(1)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2b0b6ed5ced8ee79aa5a0351ac5b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449c9623d6410aa84fa705d25069acdf.png)
您最近一年使用:0次
2023-02-10更新
|
903次组卷
|
6卷引用:湖南省长沙市宁乡市第一高级中学2022-2023学年高三上学期12月月考数学试题
湖南省长沙市宁乡市第一高级中学2022-2023学年高三上学期12月月考数学试题广东省新高考2023届高三下学期开学调研数学试题广东省东莞市海德实验学校2022-2023学年高二下学期第一次月考(3月)数学试题(已下线)拓展五:利用导数证明不等式的9种方法总结-【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第二册)新疆乌鲁木齐市第十二中学2022-2023学年高二下学期期中数学试题黑龙江省七台河市勃利县高级中学2023-2024学年高三上学期9月月考数学试题
名校
解题方法
2 . 已知函数
.
(1)求证:
;
(2)证明:当
,
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120ba271c6dd7bc66c1d27366d5ee68c.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/256f3981024e53f373a80aad40e994ae.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96d8194a129e25082d16116d7abf8452.png)
您最近一年使用:0次
2022-11-25更新
|
376次组卷
|
2卷引用:四川省江油中学2022-2023学年高三上学期第三次阶段考试数学(文)试题
解题方法
3 . 已知函数
.
(1)证明不等式:
,
;
(2)若
,
,使得
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e41217f3039effba4b352e7ae68deb.png)
(1)证明不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a623d70dccf0773e19310b4cc863fbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be23b1d40d59f429f2f90c814815491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cd6f48770212bd0382da5dbab6d95c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d136fd3c66c833cc3cf80cbf0b2870b1.png)
您最近一年使用:0次
2022-12-09更新
|
331次组卷
|
2卷引用:广西贵港市2023届高三毕业班上学期12月模拟考试数学(理)试题
名校
解题方法
4 . 已知函数
.
(1)求证:函数
在定义域上单调递增;
(2)设区间
(其中
),证明:存在实数
,使得函数
在区间I上总存在极值点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da85eb544f1b8ff532d4c2a3c8764d0f.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e07062bde69560336def001c925eb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb9dfa7ecdfa37e643c51193a388836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d8047f0a8bd0cf4e250cd0fe80093b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbd86a6b6493a67696125835eea5f76.png)
您最近一年使用:0次
5 . 已知函数
.
(1)若
在
上单调递增,求实数a的取值范围;
(2)当
时.
(i)求证:函数
在
上单调递增;
(ii)设区间
(其中
),证明:存在实数
,使得函数
在区间I上总存在极值点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef290c72466c30bc20d7414418cfaee.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754cc9374c8193dadb6875fb8a3fefb.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(i)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1899b95e2442b6a08a5a134b36ed7c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754cc9374c8193dadb6875fb8a3fefb.png)
(ii)设区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e07062bde69560336def001c925eb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb9dfa7ecdfa37e643c51193a388836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d8047f0a8bd0cf4e250cd0fe80093b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbd86a6b6493a67696125835eea5f76.png)
您最近一年使用:0次
2022高三·全国·专题练习
名校
解题方法
6 . 已知函数
,其中
为实常数.
(1)若函数
定义域内恒成立,求
的取值范围;
(2)证明:当
时,
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81efb3e3a475947efd2946029b319108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb5e28d0cce973a243074aab15c6a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1eb50f57c5ebfcf27a5f5511ccfc8f9.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1210aaa8a56ea8024de16b87cf12538f.png)
您最近一年使用:0次
2022高三·全国·专题练习
7 . 已知函数
,
,在点
处的切线方程记为
,令
.
(1)设函数
的图象与
轴正半轴相交于
,
在点
处的切线为
,证明:曲线
上的点都不在直线
的上方;
(2)关于
的方程
为正实数)有两个实根
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db9ae6e655cae4fbc0f5591329ecd464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65f426baa7cc50d42c9eb47cbcff65a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5f4dffc65e0fc5d24367a9d4e5c997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f492a6d35db1c62b0a4411f741235a96.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907085c87a6b33ce4b84c86210f9a521.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/877d540cfbe3cd131d513d4da1250a64.png)
您最近一年使用:0次
解题方法
8 . 已知函数
.
(1)当
,证明:
;
(2)设
,若
,且
(
),求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02216fa640ac5c29f59d89996af0878.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e014af902e08992a777dd225d0ca05c1.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00210f79b04a8f6bc1922433d00bc89a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3397a23ca37fd94fdf0e0ed60be9ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a415767156945ea8ada9ed3756019fc.png)
您最近一年使用:0次
名校
9 . 已知函数
.
(1)若曲线
在点
处的切线方程为
,求
的值;
(2)当
时,求证:
;
(3)设函数
,其中
为实常数,试讨论函数
的零点个数,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b195180c8b0c44ad2e6b636b36ec7b.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e79b26f3249ec0542512531174ee81a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02e32435aa5b57a34ed4a39b07c5530.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54379f19d73876e7c43b08bd9f08bf16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
您最近一年使用:0次
2019-12-30更新
|
1067次组卷
|
5卷引用:天津市实验中学2022届高三下学期高考前热身训练数学试题
天津市实验中学2022届高三下学期高考前热身训练数学试题江苏省苏州市五校2019-2020学年高三上学期12月月考数学试卷2020届江苏省南京市十三中高三下学期期初考试数学试题(已下线)专题16 函数的零点-2021届江苏省新高考数学大讲坛大一轮复习天津市第四中学2023届高三高考热身数学试题
名校
10 . (1)证明:当
时,
;
(2)若不等式
对任意的正实数
恒成立,求正实数
的取值范围;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7e5b12719915c134ab756cb09f75c1.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a264a7259b8956b59ef9ef37c9af8855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01a0805acb0016f9851d5d1a49e2b553.png)
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2017-05-22更新
|
507次组卷
|
3卷引用:陕西省西安交通大学第二附属中学2022届高三下学期第三次月考理科数学试题