名校
解题方法
1 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06678b48ba1d12f0748bbed1a9d27478.png)
(1)若
,证明:
;
(2)设
,若
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06678b48ba1d12f0748bbed1a9d27478.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62b74522d84abe0dc4d5983694ea748.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1411c719bc69f11b60e566baa09f383c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4fe5e35859136dafc3373c01009f24.png)
您最近一年使用:0次
2023-09-29更新
|
2060次组卷
|
4卷引用:辽宁省沈阳市东北育才学校2024届高三第三次模拟考试数学试题
辽宁省沈阳市东北育才学校2024届高三第三次模拟考试数学试题湖北省武汉市华中师范大学第一附属中学2023届高三5月适应性考试数学试题(已下线)第六章 导数与不等式恒成立问题 专题六 单变量恒成立之参变分离法 微点4 单变量恒成立之同构或放缩后参变分离综合训练吉林省松原市前郭尔罗斯蒙古族自治县第五高级中学2023-2024学年高三上学期10月月考数学试题
解题方法
2 . 已知函数
.
(1)若
,讨论函数
的单调性和极值情况;
(2)若
,求证:当
时,
;
(3)若
,求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b3de8a032a7081161352b34ee7bc59.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933436a516df078f4c4250d698310c13.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5a81a39630f05d9a470c1f4b3c5e524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
您最近一年使用:0次
3 . 已知函数
,曲线
在点
处的切线方程为
.
(1)求
的值并讨论
的单调性;
(2)设
为两个不相等的正数,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c99bede9abb43cf6dabb90a0cc80c4c5.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/c50866229ec5a3640fb250f9bd2192b3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/000eef050602fcd0f24777edaeab3544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4844d12d7b0a4c6bcdc3e3ab5709fe.png)
您最近一年使用:0次
2023-08-23更新
|
231次组卷
|
2卷引用:辽宁省大连市大连开发区十中2024届高三上学期期中数学试题
名校
4 . 设方程
有三个实数根
.
(1)求
的取值范围;
(2)请在以下两个问题中任选一个进行作答,注意选的序号不同,该题得分不同.若选①则该小问满分4分,若选②则该小问满分9分.
①证明:
;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b513d7bdd17b6ead5295a0400d0ab15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2755e84aeb379e0117e278f71ca0a9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)请在以下两个问题中任选一个进行作答,注意选的序号不同,该题得分不同.若选①则该小问满分4分,若选②则该小问满分9分.
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5600c61eb9170becdd342ee5619d412d.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af8a6b51796f510821931ea6a9d9cc50.png)
您最近一年使用:0次
名校
5 . 已知函数
,
.
(1)若不等式
恒成立,求a的取值范围;
(2)若
时,存在4个不同实数
满足
.证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7525c9480d4b7ac129996dbd7b1cb7cb.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9699d5af88ccdcccc1fd0cdce6018ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4a18c09f0055baa3e0abcbc75a84ed.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa939782348f031b9aba60c05fb13187.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/908bfb759e6375da922bbb1d1a028ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7525c9480d4b7ac129996dbd7b1cb7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377df1441214a18e60de35e5df609cfe.png)
您最近一年使用:0次
2023-05-25更新
|
402次组卷
|
2卷引用:辽宁省铁岭市昌图县第一高级中学2022-2023学年高二下学期6月月考数学试题
6 . 已知函数
.
(1)若
在
上单调递增,求实数
的取值范围.
(2)已知方程
有两个不相等的实数根
,且
.
①求
的取值范围;
②若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e058fc816e9935f358b1cb90433875d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192bebeaecf1729c55efad6e749a04e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae0a96799a6ffd8d340951b9db8da6d.png)
您最近一年使用:0次
解题方法
7 . 已知
为函数
的极值点.
(1)求
;
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ca79c133d3ed69b748f22369887fdf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fecaefda8567646f10d76668293d845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad9a72052450fae121d959ab6cce1817.png)
您最近一年使用:0次
名校
8 . 已知函数
,
.
(1)当
时,讨论方程
解的个数;
(2)当
时,
有两个极值点
,
,且
,若
,证明:
(i)
;
(ii)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b4f583a21e8774680dacc43ca7cd23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c944c1c2791f64d1f371d43e9a419983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db3e49df811c97550d42912410771d1.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc9920abcee41ad09f346eeb981b9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d032f4b2ba5c86e3587b195d32b10c8.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/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d51a019839f799edfeba6d696c6d6c.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204c481a567855d042f3619351f71ffa.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5fc1157c75a6fefd470508dd0c77365.png)
您最近一年使用:0次
2023-04-30更新
|
2203次组卷
|
6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
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辽宁省沈阳市第二中学2023-2024学年高三上学期10月月考数学试题山东省泰安市2023届高三二模数学试题(已下线)专题突破卷08 极值点偏移(已下线)重难点突破06 双变量问题(六大题型)(已下线)模块四 专题1 期中重组篇(辽宁卷)(人教B版高二下学期)
9 . 已知函数
.
(1)若
,求
的图象在
处的切线方程;
(2)若
有两个极值点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb41724d9a030cc2694a58dee5387494.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b725fdc8de9800f2692f6fea8585b1e9.png)
您最近一年使用:0次
2023-07-07更新
|
470次组卷
|
5卷引用:辽宁省辽阳市2022-2023学年高二下学期期末考试数学试题
10 . 已知函数
.
(1)讨论函数
的单调性;
(2)设函数
有两个极值点
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1989e8861b4406a727611680e04d29c8.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4670b3ef4895f7c5a0fe0dfeca08c922.png)
您最近一年使用:0次