名校
1 . 已知函数
.
(1)当
时,求
在
处的切线方程;
(2)若
存在大于
的零点
,设
的极值点为
;
①求
的取值范围;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ac2c352e601b8b19855cba1b17f7d36.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5f0727c115e4d6915d8dee70de54c1.png)
您最近一年使用:0次
2023-05-02更新
|
255次组卷
|
3卷引用:信息必刷卷05(天津专用)
名校
解题方法
2 . 已知函数
,
.
(1)若
,求函数
的最小值及取得最小值时的
值;
(2)求证:
;
(3)若函数
对
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0ff7ac083b888d0055e49bf130a6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950581caec90a28b5fa8f1e81bf21d19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868715c60832e7661d59fc27a18260b.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dc79bbf9c20ff70c4a152c6f7f026fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
您最近一年使用:0次
2023-04-25更新
|
2012次组卷
|
4卷引用:天津市河西区2023届高三二模数学试题
3 . 已知曲线
在点
处的切线方程为
.
(1)求a,c的值;
(2)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7823aa2ac66c00ce0f260f3147eb6a.png)
(3)若关于x的方程
有两个实数解
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e34dc94a3d9dc4677f75e0aac8e98da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96f623802cd414e590247155ad0d62b.png)
(1)求a,c的值;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7823aa2ac66c00ce0f260f3147eb6a.png)
(3)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5809a06357f94fc7a2156c7e7af1ed2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c9639ad329a88d242c2d6f37d7c456.png)
您最近一年使用:0次
2023-04-03更新
|
299次组卷
|
2卷引用:天津市实验中学2023-2024学年高三上学期9月统练数学试题
名校
解题方法
4 . 设函数
.
(1)当
时,若函数
在其定义域内单调递增.求b的取值范围;
(2)若
有两个零点
,
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a6999eea23ebccc533ed84fb3a97b4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](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/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3951a7bf1d9ca025aeef96c5c60411bd.png)
您最近一年使用:0次
2023-03-30更新
|
786次组卷
|
3卷引用:天津市宁河区芦台第一中学2022-2023学年高二下学期5月学情调研数学试题
2023高二·上海·专题练习
名校
5 . 已知函数
为常数,
是自然对数的底数),曲线
在点
处的切线与
轴平行.
(1)求
的值;
(2)求
的单调区间;
(3)设
,其中
为
的导函数.证明:对任意
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760d305308332774b7b78d44d07a5009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b40940b4fd4d0a4c2aa886bc70ec1c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d29c5c266a6d834a244c1f50c8f9848c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d875692984acee55866d1fccafa75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2495c66dd202153fcdad0e2a34abf50c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db87918cf32f0efa00edbf90c9f186c3.png)
您最近一年使用:0次
2023高三·全国·专题练习
名校
6 . 设函数
.
(1)若
在点
处的切线斜率为
,求a的值;
(2)当
时,求
的单调区间;
(3)若
,求证:在
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2559bd883fdcf66dd5f42926338761f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea59cee971344ed593ff082a65d177c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92be82894508d5fd942f8933e736b728.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62cf62a02057141c8d8665aea1bd9ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acda6b6464db27e1ec18a1522406d2.png)
您最近一年使用:0次
2023-03-27更新
|
2189次组卷
|
4卷引用:天津市第二南开学校2022-2023学年高二下学期期中数学试题
天津市第二南开学校2022-2023学年高二下学期期中数学试题(已下线)第二篇 函数与导数专题3 洛必达法则 微点2 洛必达法则综合训练(已下线)数学(全国乙卷理科)陕西省西安建筑科技大学附属中学2022-2023学年高二下学期期中理科数学试题
7 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c3876a78d1c0f3b0eb07825c34d1a5d.png)
(1)若
,过点
作曲线
的切线l,求切线l的方程;
(2)若
,
是函数
的两个不同的极值点,求证:
;
(3)
时,
对
恒成立,证明不等式
对任意的正整数n都成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c3876a78d1c0f3b0eb07825c34d1a5d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.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/051c9ada827d18c8377743299d3761df.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb9374a0245ffdcb4b23bd8bd5b662a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bad5c8a4e4bad474651c0a61de820ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fada3f2d5821bea73b3f22b25a07a8a7.png)
您最近一年使用:0次
名校
8 . 已知函数
,
.
(1)求函数
的单调区间;
(2)若函数
有唯一的极值点
,
①求实数
取值范围;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc857da96107b0e2606de28370ba775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa5a94ae1c6562a890f67f598650ad4.png)
您最近一年使用:0次
2023-03-26更新
|
1449次组卷
|
5卷引用:天津市2023届高三高考前最后一卷数学试题
名校
解题方法
9 . 已知函数
.
(1)若
,
(i)求
的极值.
(ii)设
,证明:
.
(2)证明:当
时,
有唯一的极小值点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73cf6e32e792e5161ed56349841ef9e3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531a488d57fde1a07d79b7590f964e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877835f59a9147b8ee3243af7f6e38f5.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65cc52aacc31a21a443c8de0374b24f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c052a4d10c0f6291d53bd20ca5b960b.png)
您最近一年使用:0次
2023-03-19更新
|
721次组卷
|
2卷引用:天津市武清区杨村第一中学2022-2023学年高二下学期期中数学试题
10 . 已知函数
.
(1)求
的单调区间;
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5feed39d9d05d7aea1011415e7511099.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c67ddd60c47e91783929c8bdf8ba8.png)
您最近一年使用:0次