名校
1 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb78f95705bf886cd6ecb60469e9a28.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4ec6c78bab05a5df3d9954a70846ec.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb45a2f8b4a14b62425a2561624e777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
您最近一年使用:0次
2019-12-27更新
|
1329次组卷
|
8卷引用:黑龙江省哈尔滨市第九中学2019-2020学年高三上学期第一次月考数学文科试题
黑龙江省哈尔滨市第九中学2019-2020学年高三上学期第一次月考数学文科试题贵州省贵阳市普通高中2019-2020学年高三上学期期末监测考试数学(文)试题2020届河南省高三普通高等学校招生模拟考试理科数学试题2020届福建省仙游县枫亭中学高三上学期期末数学试题(已下线)专题02 导数(文)第三篇-备战2020高考数学黄金30题系列之压轴题(新课标版)重庆市綦江中学2020-2021学年高二下学期第一次阶段性考试数学试题(已下线)专题02 导数(理)第三篇-备战2020高考数学黄金30题系列之压轴题(新课标版)四川省绵阳市南山中学实验学校2024届高三上学期“二诊”模拟数学(文)试题
12-13高三上·福建福州·期末
名校
解题方法
2 . 已知函数
,
.
(1)若函数
,求函数
的单调区间;
(2)设直线
为函数
的图象上一点
处的切线.证明:在区间
上存在唯一的
,使得直线
与曲线
相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc873fc03e6e4d3c4ba02f8b1147b20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abdb0052a30184ec7bdc7e4fbd3922c.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81730daa7f719cce05baa04bb390e901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23fb90e09994fdc6ab02ed6ba664f31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd3ffc5e95e5f22723402501c9916b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a7a4a037a4dfe973f1eb683d93d799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
您最近一年使用:0次
2020-07-22更新
|
513次组卷
|
12卷引用:黑龙江省哈尔滨市第九中学2020届高三第三次模拟考试数学(文科)试题
黑龙江省哈尔滨市第九中学2020届高三第三次模拟考试数学(文科)试题黑龙江省哈尔滨九中2020届高三高考数学(文科)三模试题(已下线)2012届福建省福州市高三第一学期期末质量检测理科数学(已下线)2012届北京市高考模拟系列试卷(二)理科数学试卷(已下线)2011-2012学年福建省龙岩一中高二第二学期期中理科数学试卷(已下线)2012届新疆克拉玛依市实验中学高三4月模拟一理科数学试卷2015届江西省上高二中高三上学期第三次月考文科数学试卷2015-2016学年重庆八中高二下第三次周考文科数学试卷吉林省通化梅河口市第五中学2022-2023学年高三上学期9月月考数学试题山东省济南市山东省实验中学2024届高三上学期第三次诊断考试数学试题江苏省苏州市南京师大苏州实验学校2024届高三上学期阶段测试(五)数学试题 山东省青岛第五十八中学2023-2024学年高二上学期阶段性测试(第二次月考)数学试卷
3 . 已知函数
.
(1)若函数
在
处的切线与直线
平行,求
的值;
(2)若函数
有两个不同的极值点
,
,且
,求证:
为自然对数的底数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb46b2bd0571a27f7458d124602fb1d.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa13f6640446773d63a2ef4347f0cd32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e06cd3daf9f501060c58d63fa31a7d.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/5e3c99ca3d73d87d3fdbef88c859dd6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae18366a24f9b7fbba485cd3b97475c.png)
您最近一年使用:0次
4 . 已知函数
(
).
(1)当
时,求函数
的图象在点
处的切线方程;
(2)若
,当
,
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca70ad64b42dfd35f9537f849c2269e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.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/bb45f673c56a289ea78831c9237e8d20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c243e508ac522c56ac59ddc410ddf99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44812d9c8644d15b85f320cfe3cee7cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acda6b6464db27e1ec18a1522406d2.png)
您最近一年使用:0次
2020-07-13更新
|
245次组卷
|
2卷引用:黑龙江省大庆第一中学2020届高三第三次模拟数学(理)试题
名校
解题方法
5 . 已知函数
,曲线
在点
处的切线方程为
.
(1)求
、
的值;
(2)求证:当
,
时,不等式
恒成立
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed9e6288c3f7fa00ed8b7a04a793b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb1feeee7cb80c1c861b6aa3f762889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7690f62e0b3a59c3ff0c31fe4033de1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe6a7d38b2e41ad995ba91415fa43ea.png)
您最近一年使用:0次
2020-05-29更新
|
275次组卷
|
2卷引用:黑龙江省哈尔滨市哈尔滨师范大学附属中学2022-2023学年高三上学期开学考试数学试题
6 . 已知函数
.
(1)若曲线
与直线
相切,求实数
的值;
(2)若函数
有两个零点
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ae1710efea13d3341cdc8c84f40f44.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baabfd32465e9e50409413d9c1358279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.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/40c67a34394380636fdf4b882ce28d40.png)
您最近一年使用:0次
名校
7 . 已知函数
.
(1)当
时,求函数
在
处的切线方程;
(2)若函数
的两个零点分别为
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/275d485cc5743c7b684412b0afd8b7ff.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35cca7268f18e3ea78e6dbc9181e679b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c81965854dbe52a513241f196edf2c.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba9520e2faffc5df03e0c9c2ff8f274.png)
您最近一年使用:0次
2019-11-12更新
|
705次组卷
|
2卷引用:黑龙江省大庆市2019-2020学年高三第一次教学质量检测数学(理)试题
名校
解题方法
8 . 已知函数
,函数图象上有两动点
、
.
(1)用
表示在点
处的切线方程;
(2)若动直线
在
轴上的截距恒等于
,函数在
、
两点处的切线交于点
,求证:点
的纵坐标为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108c18cb76d7d34b05c991a644c8b136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2020-05-16更新
|
323次组卷
|
2卷引用:黑龙江省哈尔滨市师大附中2019-2020学年高二下学期期中考试数学(理)试题
名校
解题方法
9 . 已知函数
,且曲线
在
处的切线斜率为
.
(1)求实数
的值;
(2)证明:当
时,
;
(3)若数列
满足
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb15aecf69d1ba00f68603ddc6d71491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e6f6556690a0720e9cea1ddf7b9028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92903b4ad4fc018c9f7d0309ed20403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7dd6a0a95be9a07ab8f7db6cbf2b42d.png)
您最近一年使用:0次
2020-09-05更新
|
1996次组卷
|
6卷引用:黑龙江省鹤岗市第一中学2020-2021学年高三上学期第二次月考数学(理)试题
名校
解题方法
10 . 已知函数
,
,曲线
在点
处的切线与
轴垂直;
(1)求
的值;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3acc77a1f1a81ac9c42842705bb70861.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc4ce237aca19aca1eb5d062f98315f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74194dfa98b8ae62e0dd5eb5bbc7f89f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4257199cd2c52c8e9e4be68866ae761.png)
您最近一年使用:0次