名校
1 . 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
|
651次组卷
|
14卷引用:福建省宁化第一中学2022届高三9月第二次月考数学试题
福建省宁化第一中学2022届高三9月第二次月考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云南衡水实验中学2022届高三上学期期中考试数学(理)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)
解题方法
2 . 已知函数
,记曲线
在点
处的切线为
,
在x轴上的截距为
.
(1)当
,
时,求切线方程;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e70f9d551b5436e708b405268ea290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27c0ab3e2d7698f082854bafe4174dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126a0b15e6d9d6c106cdc3aa74a83cd3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d47b5d9bb960850cfc33e252d3d852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266115b42426704177393dff1db45f00.png)
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名校
3 . 设函数
.
(1)求曲线
在
处的切线方程;
(2)证明:当
时,
恒成立;
(3)证明:当
且
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ec0e4f8ac671c9e93a3ce7495aecad.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2c84e7b41a841a230ed5f8a42309aa.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dc63725756ed048cebe7043720f5cb.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fbc202b50ed7c7a40ca321471d1790f.png)
您最近一年使用:0次
2023-05-15更新
|
477次组卷
|
2卷引用:福建省莆田第四中学2023-2024学年高二下学期期中考试数学试卷
解题方法
4 . 已知函数
,其中
,曲线
在
处的切线
与坐标轴围成的面积为
.
(1)求实数
的值;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e577bb4766762598258778e390b30b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ec226fe3bfcbba33151cfff9a2603d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/868e738c6de3d68c0eb90984874a8640.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d07f9b89b24792b5e5cc639b399ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b7291b07859babc65e950cf6913ee6.png)
您最近一年使用:0次
名校
解题方法
5 . 已知
在
处的切线方程为
.
(1)求函数
的解析式:
(2)
是
的导函数,证明:对任意
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9303148aba05dd1276ec04cad34e857d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a2b4c212450b2a0f77e042c8da13dd.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4606e82c8df971bd7803c532c58b7a00.png)
您最近一年使用:0次
2023-02-19更新
|
975次组卷
|
6卷引用:福建省漳州市第五中学2022-2023年高二下学期期中考试数学试题
6 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fe7bbc9dac37c7717e5137168acc63.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1164131f59bd05d660deb2b0810591.png)
(1)已知f(x)在点(1,f(1))处的切线方程为
,求实数a的值;
(2)已知f(x)在定义域上是增函数,求实数a的取值范围.
(3)已知
有两个零点
,
,求实数a的取值范围并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1164131f59bd05d660deb2b0810591.png)
(1)已知f(x)在点(1,f(1))处的切线方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
(2)已知f(x)在定义域上是增函数,求实数a的取值范围.
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9bcff3889d445230323de77818a824.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/1b4900c67f4b57fa430c4bd863f8e896.png)
您最近一年使用:0次
2023-05-31更新
|
2400次组卷
|
7卷引用:福建省厦门市湖里区双十中学2022-2023学年高二下学期6月月考数学试题
福建省厦门市湖里区双十中学2022-2023学年高二下学期6月月考数学试题北京市通州区2023届高三考前查漏补缺数学试题(已下线)重难点突破05 极值点偏移问题与拐点偏移问题(七大题型)-1(已下线)专题12 导数及其应用(已下线)专题2-6 导数大题证明不等式归类-3(已下线)模块三 大招16 极值点&拐点偏移(已下线)考点21 导数的应用--极值点偏移问题 2024届高考数学考点总动员【练】
名校
8 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/959378c05b4a0005e19879d39bd7560d.png)
,其中e为自然对数的底数.
(1)求曲线
在点
处的切线方程;
(2)当
时,有
,求证:对
,有
;
(3)若
,且
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d923750277c4ae4f8a7db57254c635b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/959378c05b4a0005e19879d39bd7560d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d52d0c48d830f5f7c50a0fdedc9b0ca7.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d29c5c266a6d834a244c1f50c8f9848c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f68ece0e49af68f032bd8a9229fbe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1c20dd78642c78b87a0d7453b507af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f86927f31837cf11baf247c14ca372d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561d31d39ae40692dd819c46a20beffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf1471ecf1a536fb4d911fd5da261448.png)
您最近一年使用:0次
2022-11-16更新
|
598次组卷
|
5卷引用:福建省宁德第一中学2022-2023学年高二下学期5月月考数学试题
福建省宁德第一中学2022-2023学年高二下学期5月月考数学试题四川省遂宁市2023届高三零诊考试数学(理科)试题四川省遂宁市射洪中学校2022-2023学年高三上学期零诊数学试题(理)(已下线)专题10 导数压轴解答题(综合类)-1(已下线)第六章 导数与不等式恒成立问题 专题十二 恒成立问题综合训练
9 . 已知函数
.
(1)若
,求函数
的图像在
处的切线方程;
(2)若
,
是函数
的两个极值点,求
的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/873b9262b539ce8d5dedd2abb1d391d5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若
![](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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9088310f1b06d5f580e99b2660f1902.png)
您最近一年使用:0次
2023-05-19更新
|
451次组卷
|
4卷引用:福建省宁德市福鼎第六中学2022-2023学年高二下学期6月月考数学试题
名校
解题方法
10 . 设函数
.
(1)若
,求证:
;
(2)设函数
,直线
与曲线
及
都相切,且
与
切点的横坐标为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f4f70194c44144fca274e7986f030c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a008acdbba2088e258dbede874f16d.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbb87a8b7ab6184b7c2787b4a5e365c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2125278e64e562b4906e3923a330f5c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e684d1e3909f08ce928c68dd3e35122.png)
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2022-10-11更新
|
211次组卷
|
2卷引用:福建省厦门外国语学校2023届高三上学期10月月考数学试题