1 . 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
2 . 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
名校
解题方法
3 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)求函数
在
上的最大值和最小值;
(3)设
,证明:对任意的
,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9de663b1fa8c103874079c5887b83b.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e205a5122e143150e455f69bff98a650.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469f9653302200578214e3372c6e7d7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c58c1659dffbd5bd9e2428641dfd022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e320f0a2c68ef9a4bfa8d9aa9da6e9a.png)
您最近一年使用:0次
2023-04-11更新
|
1298次组卷
|
4卷引用:福建省南安市柳城中学2022-2023学年高二下学期期中数学试题
4 . 设函数
.
(1)若
,求函数
在点
处的切线方程;
(2)试判断
的零点个数,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018afcc369a0cbec2ca55a75dee23f94.png)
(1)若
![](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/81158db42116f74e7b26e100f88dd535.png)
(2)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/befa604ab2e23a0b1fbc1e364e95e27a.png)
您最近一年使用:0次
2022-09-24更新
|
456次组卷
|
4卷引用:福建省福州高级中学2021-2022学年高二下学期第四学段(期末)考试数学试题
福建省福州高级中学2021-2022学年高二下学期第四学段(期末)考试数学试题江西省赣州市赣县第三中学2023届高一上学期10月月考数学(文)试题江西省赣州市赣县第三中学2022-2023学年高一上学期10月月考数学(理)试题(已下线)第五章 一元函数的导数及其应用(A卷·知识通关练)(5)
5 . 设函数
,函数
,其中
,(
是自然对数的底数).
(1)求函数
在
处的切线方程;
(2)记函数
的最小值为
. 求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b26f55c7c29644dfe0277d3e2adf10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/275def986ac0cb401d6fdc2473acb119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187c21027ff08411931d32c530b64fd3.png)
(2)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed22acda3591f67e9fbffe3fd6112a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f22a5e113580f63448e650e94134fbb.png)
您最近一年使用:0次
6 . 已知函数
,设曲线
在点
处的切线与x轴的交点为
,其中
为正实数.
(1)用
表示
;
(2)若
,记
证明数列
成等比数列,并求数列
的通项公式.
(3)若
,
是数列
的前n项和,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7b0deaff280ebbee0f91be5acd20d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641fec779880f75fa8ee6782f3350402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edeb4aa8a3ca0261e0161fd7fa8bde97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002f56900c2924bfd79fc3865b0a02e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4223bd6ee8f82d59d244371fbcddc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfe65f891c54780bcf1ed6a9f8a0f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1abbe79bea9a630a3ac5db989f44d7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3819480e1e624208f729ad8653e4f24f.png)
您最近一年使用:0次
2022-11-24更新
|
1124次组卷
|
3卷引用:福建省永春第一中学2022-2023学年高二上学期期末考试数学试题
名校
7 . 已知函数
,
(1)求函数
在
处的切线方程;
(2)若函数
在区间
内有唯一极值点
,解答以下问题:
(i)求实数a的取值范围;
(ii)证明:
在区间
内有唯一零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53db73b6d8b8cea2421dabd955f146ef.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f00f2f6ab162f9333ec55db195d663b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
(i)求实数a的取值范围;
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ff8dca35b759d3051b62badd7d76bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddcd777d9a19b5d4016fef6a0650cb85.png)
您最近一年使用:0次
2022-12-15更新
|
694次组卷
|
5卷引用:福建省上杭县第二中学2023届高三上学期12月月考数学试题
福建省上杭县第二中学2023届高三上学期12月月考数学试题福建省福州市八县(市、区)一中2023届高三上学期期中联考数学试题(已下线)上海市华东师范大学第二附属中学2022-2023学年高二下学期5月月考数学试题(已下线)第九章 导数与三角函数的联袂 专题四 利用导数证明含三角函数的不等式 微点3 利用导数证明含三角函数的不等式(三)(已下线)专题05导数及其应用--高二期末考点大串讲(沪教版2020选修)
名校
8 . 已知函数
(
,e为自然对数的底数).
(1)若
在x=0处的切线与直线y=ax垂直,求a的值;
(2)讨论函数
的单调性;
(3)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39c7d502016162b581464297f7444d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324c5822114cf4bf2063fb2ddaa27e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f8ae199db6fb88d06f9b40c4937f71.png)
您最近一年使用:0次
2022-04-08更新
|
1322次组卷
|
6卷引用:福建省莆田第二十五中学2021-2022学年高二下学期期中考试数学试题
名校
解题方法
9 . 已知
是函数
的一条切线,
,且
是
的导数.
(1)求
的值;
(2)证明:当
,
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb70fdf064b9193e506ca43f4672af56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a982990e6a65123ec91baba94168ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b1c10ac0d5434396a941a27c5cf668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51350a90203fcdc2d500a89061b7f52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02d1c039d9420ce3f9b3e9d58ab08d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bb5ac10a2ab38b9f4c31a318422a4c.png)
您最近一年使用:0次
2022-05-12更新
|
590次组卷
|
3卷引用:福建省厦门第一中学2021-2022学年高二下学期期中考试数学试题
福建省厦门第一中学2021-2022学年高二下学期期中考试数学试题(已下线)期末押题预测卷01(考试范围:选修二+选修三)-2021-2022学年高二数学下学期期末必考题型归纳及过关测试(人教A版2019)广东省潮州市饶平县第二中学2021-2022学年高二下学期月考(二)数学试题
10 . 已知函数
和
.
(1)求
在
处的切线方程;
(2)证明:存在直线
,其与两条曲线
和
共有三个不同的交点,并且从左到右的三个交点的横坐标成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5b73240b061499bb52ee932362dcba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e275bb972163df5318c87a8c89f6379e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5b73240b061499bb52ee932362dcba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffe604dac7e511c06aa339460743ba0.png)
(2)证明:存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af79f45b5880c72a349500da9d8e118d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
您最近一年使用:0次