名校
解题方法
1 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1b70d8169a0264375fb4cc7b85a011.png)
(1)若函数
与
的图象存在公切线,求
的取值范围;
(2)若方程
有两个不同的实根
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1b70d8169a0264375fb4cc7b85a011.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576469e4f51c1ede73f7f0458f504418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f03fd662f69ce3e5449c08e00b963194.png)
您最近一年使用:0次
2 . 已知函数
,在点
处切线方程为
.
(1)求实数
的值;
(2)讨论
的单调性;
(3)设
为两个不相等的正数,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd403f29997195ac8a6e715f98815a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f6ed76662695d4c711be57a16c3197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca13a93b5f401c0d39ba52b0cffcb0.png)
您最近一年使用:0次
名校
3 . 已知函数
.
(1)求曲线
在点(2,2)的切线方程;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b636844dddba5c8e2a96f34e03c7eddb.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7376dbe3af5f7132e15d0457ac4ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4be9f060f0bad0cd74aed6d3a517e1c5.png)
您最近一年使用:0次
2023-04-14更新
|
262次组卷
|
2卷引用:福建省福州第一中学2022-2023学年高二下学期第三学段模块考试(期中)数学试题
名校
4 . 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
|
478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
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
名校
解题方法
6 . 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
7 . 已知
,
,函数
,
,且曲线
与曲线
在
处有相同的切线.
(1)求
,
的值;
(2)证明:当
时,曲线
恒在曲线
的下方.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b1131b5a68b32ad67f8e07bddaeb54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389a2e79c9a60b95cf47759f99fc494.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e30c903d8f8a05332af0b19e7e40df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
您最近一年使用:0次
8 . 已知函数
.
(1)求曲线
在
处的切线方程;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fdc487d4cf65c82a40b7944024f5a6.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0091fa7b5fdbffbefc27ec6e68510a.png)
您最近一年使用:0次
2022-11-20更新
|
462次组卷
|
4卷引用:福建省南平市浦城县第三中学2023届高三上学期期中测试数学模拟卷试题(1)
9 . 已知函数
,
.
(1)若直线
与曲线
和
都相切,求实数
的值;
(2)设函数
,若函数
在
上有三个不同的零点
,
,
,且
,求证:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c1184d6ad1561983ff8f46fd89bfb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bee434ff4fd518929665cf357d166ff.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73fff204cd3dff03d9ee7f63f33e0b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28eb47bf11a209a6521e16bbed6cbdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c520eb8fcc167698440cdee316134c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95123c0c6f46730b8395f5f131d1e4a1.png)
您最近一年使用:0次
2022-11-20更新
|
119次组卷
|
2卷引用:福建省南平市浦城县第三中学2023届高三上学期期中测试数学模拟卷试题(2)
名校
10 . 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