名校
1 . 已知函数
.
(Ⅰ)当
时,求曲线
在点
处的切线方程;
(Ⅱ)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97a6ef47e265de6536d94a2c3c090bd.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb1feeee7cb80c1c861b6aa3f762889.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d191d6de821fbb06a51b5a20112db6de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
您最近一年使用:0次
2016-12-04更新
|
2769次组卷
|
11卷引用:内蒙古呼和浩特市土默特左旗第一中学2019-2020学年高二下学期期中考试数学(理)试题
内蒙古呼和浩特市土默特左旗第一中学2019-2020学年高二下学期期中考试数学(理)试题2016届广东省广州市普通高中毕业班综合测试一文科数学试卷山东省济南第一中学2018届高三1月月考数学(文)试题湖北省长望浏宁四县2018年高三3月联合调研考试数学文试题【全国百强校】河北省衡水市武邑中学2018年高三高考三模数学(文科)试题【全国百强校】山东省济南外国语学校2019届高三12月月考数学(文)试题河北省武邑中学2018届高三下学期第三次质量检测数学(文)试题黑龙江省大庆市第四中学2020届高三上学期第一次检测数学(文)试题北京实验学校(海淀)2019-2020 学年度高二下学期期末考试数学试题四川省南充市2021届高三第三次模拟考试数学(文)试题福建省福州高新区第一中学2024届高三上学期第一次月考数学试题
解题方法
2 . 已知函数
,
,
.
(1)当
时,存在
,
,使得
成立,求实数
的取值范围;
(2)证明:当
时,对任意
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157e9a31c8e0184a70758218fcc89465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b05282c9456a228cee2b7a9c3591e73.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ffb8594d1244f3602521be12cae6e3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dbf1fe017d40404855fe73d4f18261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133cb4bfa780967fce1ef6181f2cf545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b89c33bf8803c80b65d4ebd7746645e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966b60302d80d8613675bb3dd5c03164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6849a4187dcbd6a9fddb8541dae50b00.png)
您最近一年使用:0次
名校
3 . 已知函数
,
.
Ⅰ
当
时,讨论函数
的单调性;
Ⅱ
若函数
有两个极值点
,
,且
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a54d0a24a4255288620cd8d1c820b03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ebfef550eec07598671c5929259780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901e166950982904f9720a258ec3f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040135d64192de075ba0cc9f11ddbc9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa33c2bd791339d32821077846605d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6fe150b0a721696c8c063999ba38d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5988baee08308b60e00a50679d746018.png)
您最近一年使用:0次
2019-04-10更新
|
867次组卷
|
5卷引用:【市级联考】内蒙古呼和浩特市2019届高三3月第一次质量普查调研考试数学(理)试题
解题方法
4 . 已知函数
(
且
)的零点是
.
(1)设曲线
在零点处的切线斜率分别为
,判断
的单调性;
(2)设
是
的极值点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17df04e44071ea7a112457552f8c3e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(1)设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31cdc61764eef3fbe2dc5fafaa2efb39.png)
您最近一年使用:0次
解题方法
5 . 已知函数
.
(1)求证:
;
(2)函数
,有两个不同的零点
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795d5a268c1052d9e34b7b57e0719950.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0c5c350e878bb52c2997f29da230b3.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/6fa6bae4c1d5d2d92effd98b8c40dd5f.png)
您最近一年使用:0次
2020-11-22更新
|
529次组卷
|
2卷引用:内蒙古呼和浩特市2021届高三质量普查调研考试理科数学试题
6 . 设
,且
,记
,
,
,则
,
,
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0db1270306500251e8d691a9a5b78f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9876508125ddd5d3e7e5519ddb6bd3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5651dccea3fb50871e9229556563c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc57f62fc5fb9c142ed8948b6a4aaa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679f440713ccea6351673679c41791d5.png)
![](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/071a7e733d466949ac935b4b8ee8d183.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-02-26更新
|
498次组卷
|
4卷引用:2020届内蒙古包头市高三上学期期末教学质量检测数学理科试题
名校
7 . 已知函数
.
(1)求函数
在点
处的切线方程;
(2)若函数
只有一个极值点,求实数
的取值范围;
(3)若函数
(其中
)有两个极值点,分别为
,
,且
在区间
上恒成立,证明:不等式
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca47d2e8724200bf868215c66c5cfe40.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/903e63d4a34cc16c1f28b66298272889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d12d46d386c33dc0f9abcafb323c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db1b7b5e4953a249b88d2eec36364af.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/e2613fa3f3008e09c1204631b4b2c0d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694dc2a9102d1272d75be70a81bab75e.png)
您最近一年使用:0次
2020-01-12更新
|
505次组卷
|
4卷引用:内蒙古自治区乌兰察布市等五市2019-2020学年高三上学期期末数学试题
8 . 已知二次函数
.
(1)讨论函数
的单调性;
(2)设函数
,记
为函数
极大值点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5397ee1eb6d157f6ec1e7a878f8d16e.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82135c13ccefdcf4da4ef15942e5c92f.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4915d641a6b011c0d6aa674215295b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183d255d42754146d4ae1f875f77644c.png)
您最近一年使用:0次
2018-04-05更新
|
1043次组卷
|
2卷引用:内蒙古呼和浩特市2018届高三第一次质量调研普查考试数学(理)试题
名校
解题方法
9 . 已知函数
,
.
(1)求函数
的极值;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdef69e49248f431b018037d8c4e3d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a1e76a990e884cc88eac704b1d892c.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a591fad70a67ee9c120623e4b7b7915.png)
您最近一年使用:0次
2020-07-30更新
|
449次组卷
|
2卷引用:内蒙古通辽市开鲁县第一中学2020-2021学年高三上学期第一次月考数学(文)试题
10 . 已知函数
.
(1)设
,求函数
的单调区间,并证明函数
有唯一零点.
(2)若函数
在区间
上不单调,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc873fc03e6e4d3c4ba02f8b1147b20.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0dcd78dea6bd95fee557c8d51ccf330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc460095ab15a43aa53e7cc058fa03d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9e3dc2e74a6af9eb262e8868d7fa2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db88ef265fa34e52d9bd847735223171.png)
您最近一年使用:0次