名校
1 . 已知函数
,
.
(1)讨论函数
的单调性;
(2)若函数
的零点分别为
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/620809df01729bc526807d556a5e2b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)讨论函数
![](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/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36a8d91a252a9aa73409835bf4214be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ef32f91e899814af999e09a8df969c.png)
您最近一年使用:0次
2023-07-12更新
|
629次组卷
|
4卷引用:江苏省南京市第一中学2023届高三下学期高考适应性考试数学试题
江苏省南京市第一中学2023届高三下学期高考适应性考试数学试题(已下线)专题09 函数与导数(解密讲义)四川省绵阳市2022-2023学年高二下学期期末数学(文)试题(已下线)模块四 专题6 暑期结束综合检测6(提升卷)
2021·江苏徐州·二模
名校
解题方法
2 . 已知函数
,
为
的导数.
(1)设函数
,求
的单调区间;
(2)若
有两个极值点
,
①求实数a的取值范围;
②证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc60033ba6dc26dfec31011590cea32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d51a8e675d11ad7ed8ecef88cdb57d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
①求实数a的取值范围;
②证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9b4d2b7cb143d8eb0e650b4b98b341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e4f81c8aef2175ff0f6b6f84be848d.png)
您最近一年使用:0次
2021-03-26更新
|
2287次组卷
|
5卷引用:江苏省七市(南通、泰州、扬州、徐州、淮安、连云港、宿迁)2021届高考三二模数学试题
(已下线)江苏省七市(南通、泰州、扬州、徐州、淮安、连云港、宿迁)2021届高考三二模数学试题黑龙江省哈尔滨第六中学2021届高三三模数学(理)试题湖北省华中师范大学第一附属中学2021届高三下学期四月综合测试数学试题重庆市第七中学2020-2021学年高二下学期期中数学试题(已下线)专题2.16 导数-不等式的证明-2021年高考数学解答题挑战满分专项训练(新高考地区专用)
名校
3 . 已知函数
,
,已知
是函数
的极值点.
(1)求曲线
在
处的切线方程,并判断函数
的零点个数;
(2)若对任意的
,
恒成立,求实数
的取值范围;
(3)设函数
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3bd98d1b43579b03aa846bb587b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d79abea823e0fe1a002fe65a9a27d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ed11c789e8852f92cf148cbf6fe6d8.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02bc62ed949c07febe3d73fdf2c8d517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec2b5fd033098f086dbabf76926a913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a75b9d4dd4b18a1e59c5fb3b45379c9.png)
您最近一年使用:0次
2022-11-16更新
|
1274次组卷
|
4卷引用:江苏省苏州市2023届高三上学期12月高考模拟数学试题
江苏省苏州市2023届高三上学期12月高考模拟数学试题天津市滨海新区塘沽第一中学2022-2023学年高三上学期第二次月考数学试题 (已下线)第5章 一元函数的导数及其应用 单元综合检测(难点)(练习)-2022-2023学年高二数学同步精品课堂(人教A版2019选择性必修第二册)重庆市第七中学校2024届高三上学期第一次月考数学试题
名校
4 . 设函数
,
.
(1)若函数
图象恰与函数
图象相切,求实数
的值;
(2)若函数
有两个极值点
,
,设点
,
,证明:
、
两点连线的斜率
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/603589540f7897790f99a8d75fd725f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5602d1637fb9dab9ef09ae6030b4ed7d.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10bb9a8107bd9c4f083578f473b9a99.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/67a3f0d7706dd7b38b770656f6937776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210304b08abfee9be4e4d3b01e323a66.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/b387bb66f74a73d9f08c79e77a4df771.png)
您最近一年使用:0次
2023-03-09更新
|
627次组卷
|
2卷引用:江苏省南通市崇川区等5地2023届高三下学期3月高考适应性考试(一)数学试题
解题方法
5 . 已知函数
.
(1)求
的最小值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b53c2a646d232372bfa28f6a5f5cb57.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b178a84b202ff0c99f4cc9e08a962e.png)
您最近一年使用:0次
名校
6 . 设函数
,其中
为自然对数的底数.
(1)当
时,讨论函数
在
上的单调性;
(2)当
时,求证:对任意
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b6ffc19f1678f3cd5a1a2687f3e8f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e445f608e4a7d8535b100c0199a8ecf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009935dae2483304749bfa46ceb6eecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2143a6cfd3526c4f5795328baa51b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/563ed1ebb56e33b5c387f3666be28fa9.png)
您最近一年使用:0次
2023-01-01更新
|
599次组卷
|
3卷引用:江苏省淮安市郑梁梅高级中学2023届高三二模数学试题
名校
解题方法
7 . 已知函数
,
,曲线
在
处的切线的斜率为
.
(1)求实数
的值;
(2)对任意的
,
恒成立,求实数
的取值范围;
(3)设方程
在区间
内的根从小到大依次为
、
、
、
、
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56ec2258720b77cd82dc6510acc563b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75f521cf86c1dd503870fa5121fcd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24db7b603aebdee8e298d1fe49c848e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a34b4bf4bba566959635a7982cec6ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c62477c656febc9646b305a64484ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)设方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29fe377ffb047b7814370ac2785257f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c8676241a10be38fec3457bd7cd1d9.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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c642de19a879df2e18cc5c5c44bd5b07.png)
您最近一年使用:0次
名校
8 . 已知函数
,其中
为实数,
为自然对数底数,
.
(1)已知函数
,
,求实数
取值的集合;
(2)已知函数
有两个不同极值点
、
,证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bb045f84f494812f0412eba6f3c161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e83eefa2d62adec7da915408483e4cd.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/334b207b056ebe4f01f5adf0a1764324.png)
您最近一年使用:0次
2023-06-16更新
|
581次组卷
|
2卷引用:江苏省镇江中学2023届高三下学期3月大练2数学试题
名校
解题方法
9 . 已知函数
(e是自然对数的底数).
(1)当
时,试判断
在
上极值点的个数;
(2)当
时,求证:对任意
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf8ebf4a2e85a082015bd76130d7c03.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/e5d6243e93c41978871cb23d8e66148d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225f4c734adee1a6b3b7ea958848b355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2184b52b7aec740fdb99470457b53483.png)
您最近一年使用:0次
2022-04-29更新
|
1224次组卷
|
5卷引用:江苏省常州市前黄高级中学2023届高三考前攀登行动(一)数学试题
10 . 设函数
,
.
(1)若直线
是曲线
的一条切线,求
的值;
(2)证明:①当
时,
;
②
,
.(
是自然对数的底数,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0ec3c50f8ff3bbb30ba0a0962073f2.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87490be8d0cdb7bc6c39d1a37f3bc335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)证明:①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb31e419ea4e0ec8f06d8cb4e348debc.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4dacb2a0080a87354011933ee07008f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25da8298b6a96d627f3e8c990e55f0c.png)
您最近一年使用:0次
2022-09-19更新
|
1125次组卷
|
4卷引用:江苏省南通市2022-2023学年高三上学期第一次质量监测数学试题