名校
解题方法
1 . 已知函数
,
是大于0的常数.记曲线
在点
处的切线为
,
在
轴上的截距为
,
.
(1)当
,
时,求切线
的方程;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad3da8a9798cf59dc08d553e342979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3423edf53e50f0b84c0a901f175f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04cefacded707b7f8c9f8b9ade6ef32c.png)
您最近一年使用:0次
2023-12-07更新
|
889次组卷
|
3卷引用:湖南省衡阳市第八中学2023-2024学年高二创新班上学期第三阶段测试数学试题
名校
解题方法
2 . 已知函数
.
(1)当
时,求
的最大值;
(2)当
时,求证:
(记
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5fd3930f9da12970ae166ebb6b1cb07.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3395c7415946c9beec09d7752650f826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2475513af67111df7a5d213692a474a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b4eae961232a89aa0680ea7422c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c52da1246020bbb227cf9a3afac354f.png)
您最近一年使用:0次
名校
解题方法
3 . 已知
.
(1)若
的最小值为
,求
的值;
(2)若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4395afaa8cf59c1fbb0daf77c6879eb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e722513658d8a5cced7c019a834162c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-02-03更新
|
1108次组卷
|
6卷引用:湖南省长沙市湖南师范大学附属中学2023-2024学年高三下学期月考七数学试题
名校
解题方法
4 . 已知函数
,
.
(1)已知
,若
时,
恒成立,求
的取值范围;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9965f0e466e76c25a895d50e1c4021f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2397df3279607612ea3cbef101ee0bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc5edf9452aa4bc39e7c6f7369785207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7eac4533a556f5a99795e210c79fd5.png)
您最近一年使用:0次
2023-03-03更新
|
860次组卷
|
2卷引用:湖南省长沙市雅礼中学2023届高三下学期月考(七)数学试题
名校
解题方法
5 . 已知函数
(
).
(1)若a=1,讨论
的单调性;
(2)若函数
存在两个极小值点
,
,求实数a的取值范围;
(3)当
时,设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d1711795e5eb438c006d1ef51755b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)若a=1,讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f80952f38d60fd6536fc48a0865ad44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee34145818988c4fb359b9e5a09732c3.png)
您最近一年使用:0次
2022-02-17更新
|
1802次组卷
|
5卷引用:湖南省六校2022届高三下学期2月联考数学试题
名校
6 . 已知函数
,且正数a,b满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45e3adfad77798d50f3cc64920fab44.png)
(1)讨论f(x)的单调性;
(2)若
的零点为
,
,且m,n满足
,求证:
.(其中
……是自然对数的底数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06e634430688fb60f1534d658f4379b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45e3adfad77798d50f3cc64920fab44.png)
(1)讨论f(x)的单调性;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a60699e3e7a4c73c8a5e4585013e4da6.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/0288311544d306cfa4b9e56ae707eeff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f145ad1f0a2e33f6d0cb48ea4caefba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405dfcca25b76af059fb4c308983eae.png)
您最近一年使用:0次
名校
7 . 已知函数
,
.
(1)讨论
的单调性;
(2)当
,
时,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d447b4a2fe1b0c37a7f9024a8abe42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f85207214ae25efd71aec5ed5e6fb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03fba6a6c02007b154015e84832eae90.png)
您最近一年使用:0次
2022-03-29更新
|
1744次组卷
|
7卷引用:湖南省长沙市雅礼中学2022届高三下学期高考前压轴(三)数学试题
名校
8 . 已知函数
.
(1)若
在
上恒成立,求
的取值范围;
(2)在(1)的条件下证明:对任意
,都有
;
(3)设
,讨论函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c5a10e26bc8668a7b20bf4e25a92bac.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)在(1)的条件下证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6aa66652d801dfe5ed77b8f196d2d49.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8736b77b6e314d1a13b16c31d9094af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4633de9335d15d7685bdecb007a3678c.png)
您最近一年使用:0次
名校
9 . 已知函数
.
(1)讨论函数
的单调区间;
(2)若曲线
在
处的切线垂直于直线
,对任意
恒成立,求实数b的最大值;
(3)若
为函数
的极值点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a32017ba8a1d4613cfd9ec6d030d016.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6765d0353d6ef706a6c3bb411138647.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd4a25c61167cd73dd176d2c39b4b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07238e4e1f21841ecc5a8daaf3b5ade.png)
您最近一年使用:0次
2023-02-18更新
|
829次组卷
|
2卷引用:湖南省长沙市麓山国际实验学校2022-2023学年高三下学期3月自主检测数学试题
名校
解题方法
10 . 已知函数
(其中
为自然对数的底数).
(1)求函数
的最小值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a5869bc299083ccc575e613798c4e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3e9ff79cc6efb6dd7c60f089f61310.png)
您最近一年使用:0次
2021-02-04更新
|
2674次组卷
|
13卷引用:湖南省名校联考联合体2021届高三下学期高考仿真演练联考数学试题
湖南省名校联考联合体2021届高三下学期高考仿真演练联考数学试题湖南省益阳市南县立达中学2022-2023学年高二上学期期中数学试题江西省赣州市2021届高三上学期期末考试数学(理)试题(已下线)大题专练训练37:导数(构造函数证明不等式2)-2021届高三数学二轮复习四川省广安市华蓥中学2021届高三2月数学(理)模拟试题(已下线)综合测试卷(巅峰版)-【新教材优创】突破满分数学之2020-2021学年高二数学重难点突破(人教A版2019选择性必修第二册)吉林省延边第二中学2020-2021学年高二下学期第一次考试月考数学(理)试题人教B版(2019) 选修第三册 必杀技 第六章 6.2.2 课时2 最值的求法四川省雅安中学2022-2023学年高二下学期3月月考数学(文)试题重庆市第一中学校2022-2023学年高二下学期3月月考数学试题重庆市南坪中学校2022-2023学年高二下学期期中数学试题山东省菏泽市郓城县第一中学2022-2023学年高二下学期第一次阶段测试数学试题吉林省松原市前郭尔罗斯蒙古族自治县第五中学2020-2021学年高二下学期期中数学试题