名校
解题方法
1 . 已知函数
.
(1)
是
的导函数,求
的最小值;
(2)证明:对任意正整数
,都有
(其中
为自然对数的底数);
(3)若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/863c24ec44174bdc5dd8ea9e67870563.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)证明:对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac19e2a797cd0a408316988a63b3755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac021f53ead484c0c5a4b587e4479e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/378262d6c1ec78505e88c563c30ddc5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
2 . 已知函数
,
(1)当
时,求函数
在
处的切线方程;
(2)讨论函数
的单调性;
(3)当函数
有两个极值点
且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5facb7583ea00e6d8db952d80557f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.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/9b384412acba251d87902ab928902f16.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当函数
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b314f6ccb0a3e4fc15685d85e55bf6.png)
您最近一年使用:0次
2023-09-05更新
|
653次组卷
|
14卷引用:广东省梅州市东山中学2022届高三上学期期中数学试题
广东省梅州市东山中学2022届高三上学期期中数学试题天津市第五十五中学2021-2022学年高三上学期10月学情调研数学试题黑龙江省哈尔滨工业大学附属中学校2021-2022学年高二上学期期末考试数学(理)试题(已下线)2020年高考天津数学高考真题变式题16-20题(已下线)第13讲 双变量问题-2022年新高考数学二轮专题突破精练河南省洛阳市洛宁县第一高级中学2022-2023学年高二下学期2月月考数学理科试题江苏省南京大学附属中学2022-2023学年高二下学期3月月考数学试题天津市五区县重点校2022-2023学年高二下学期期中联考数学试题(已下线)模块五 专题5 期中重组卷(广东)天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷2(已下线)导数专题:导数与不等式成立问题(6大题型)-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册)福建省宁化第一中学2022届高三9月第二次月考数学试题云南衡水实验中学2022届高三上学期期中考试数学(理)试题广西壮族自治区梧州市苍梧中学2022-2023学年高二下学期3月月考数学试题
3 . 已知
且
.
(1)试讨论函数
的单调性;
(2)当
时,若
有三个零点
.
①求
的范围;
②设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/340d60e3b1e2b3beb66eae8d5e812f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
(1)试讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026791a5c95b5319b744d3896c99f733.png)
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名校
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
(1)求函数
的单调区间;
(2)若
,证明:
在
上恒成立;
(3)若方程
有两个实数根
,且
,
求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8eca68c4c7478f412183aa275fc7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6adb82c401086b3536212bb06125eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f68c6ed09e483db6edf0b4caf5e252.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5809a06357f94fc7a2156c7e7af1ed2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8ca3aa2d1ba52e82613d0d65d800e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d889f2c38ab7df7a03aedb3e9d28ea7.png)
您最近一年使用:0次
2023-08-16更新
|
814次组卷
|
4卷引用:黑龙江省哈尔滨市第九中学校2024届高三上学期开学考试数学试题
黑龙江省哈尔滨市第九中学校2024届高三上学期开学考试数学试题黑龙江省哈尔滨市第九中学校2023-2024学年高三上学期开学考试数学试题(已下线)第五章 一元函数的导数及其应用(压轴题专练,精选34题)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第二册)江苏省徐州市邳州市新世纪学校2024届高三上学期统练1数学试题
5 . 已知函数.
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff73582408b512f34ecac9e8182d9902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c0a8155f5a6af42d37856f6c95a0bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac2a5a4c2c38c04f1403952266869503.png)
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名校
6 . 已知
,
.
(1)求函数
的单调区间;
(2)①容易证明
对任意的
都成立,若点
的坐标为
,
、
为函数
图像上横坐标均大于1的不同两点,试证明:
;
②数列
满足
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8b8645a4cd5e41664b349bc1d2c4ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a20457d180264f78d611dc7893d735.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)①容易证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832f2474efe89961ef41e884da7660c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f662ae83689b19b2a4a9b37a3a9b70.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4b74ed1cf474f645df5ef7100c0d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfb19f0c37a72b33083ae9319f11a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b3360833401d932ae800aefe4ae8f24.png)
您最近一年使用:0次
2023-08-03更新
|
564次组卷
|
4卷引用:上海市七宝中学2022-2023学年高二下学期期中数学试题
解题方法
7 . 已知函数
.
(1)若
在区间
上单调递减,求实数
的取值范围;
(2)若
存在两个极值点
,
.
(ⅰ)求实数
的取值范围;
(ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1d40322efc1427cf46f935febd636e6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed42f3027cbe56374812ab45b0023787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(ⅰ)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7847abd5a830ff448f260b5107ac52.png)
您最近一年使用:0次
2023-08-02更新
|
486次组卷
|
4卷引用:山东省威海市2022-2023学年高二下学期期末数学试题
山东省威海市2022-2023学年高二下学期期末数学试题(已下线)第10讲:导数期末题型突破(单调性、不等式、零点、恒成立)【人教A版(2019)】专题06导数及其应用(第二部分)-高二下学期名校期末好题汇编(已下线)重组1 高二期末真题重组卷(山东卷)B提升卷
名校
8 . 已知函数
.
(1)当
时,讨论
的单调性;
(2)令
,若
有两个不相等的实数根
.
(i)求a的取值范围;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c59ee61e811f2cbb69edcd7445e8d5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5466c28592d45ca35059382b351d583f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(i)求a的取值范围;
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0fd6297d9af0dbfaccd08a53054ec5.png)
您最近一年使用:0次
9 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb80cbd80988762324b4bda6fa8bb30a.png)
(1)若
(
为
的导函数),求函数
的单调区间;
(2)求函数
在区间
上的最大值;
(3)若函数
有两个极值点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb80cbd80988762324b4bda6fa8bb30a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585de67a3fc494297d375d339af6d153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754cc9374c8193dadb6875fb8a3fefb.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f58d4591d668b4bc32fae4faab8298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c67a34394380636fdf4b882ce28d40.png)
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解题方法
10 . 已知函数
,
且
恒成立.
(1)求
的值;
(2)证明:
.
(注:其中
为自然对数的底数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b39cd9c40fb254341b3e910829898de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0991531bd48871cbb4c27d5f27d2f311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a06acf17d7c28fa264c03224226951b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/600d1eefdf691d131c4f9720da553e8a.png)
(注:其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
您最近一年使用:0次