解题方法
1 . 已知函数
.
(1)若函数
的图象在点
处的切线方程为
,求证:
;
(2)若函数
的最小值为2,求实数a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd58e16598e6bdb3c35194af69951a2a.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4955c5adc717b7f6f0b975e0724ff5.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b6002aeb475d7c5bef504cd63390b.png)
您最近一年使用:0次
2021-08-07更新
|
169次组卷
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2卷引用:江苏省泰州市2020-2021学年高二下学期期末数学试题
2 . 已知函数
,
.
(1)当
时,求函数
的单调区间;
(2)证明:当
,
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a8b07ea637694217f78f800a82af04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77472f3de4227d06d40bbb5f41e4402.png)
您最近一年使用:0次
3 . 设
,函数
,
是函数
的导函数,
是自然对数的底数.
(1)当
时,求导函数
的最小值;
(2)若不等式
对任意
恒成立,求实数
的最大值;
(3)若函数
存在极大值与极小值,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848c33e3506416358d9f0d3ee66f67a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e6939621b8893fb3a1d1ad3343b8e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e6eec516d39005c8f0944f20e66f332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff5a8f648d375cc6ccf6649cab698c6.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7bf74e4eb8ca4fa2829e4576e4023f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e6eec516d39005c8f0944f20e66f332.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b333d8d9a7e224376f747c19bf1b8366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f8b260162c0d3e535f1611dbaa74d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
您最近一年使用:0次
2020·江苏·一模
4 . 已知函数
(其中
为自然对数的底数,
).
(1)试讨论函数
零点的个数;
(2)当
时,令
,求证:不等式
对
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0de943df08c0ad6bc565b5231989f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)试讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2825f60b300b35c0b20dad5c4f41cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04bd9759565e4cd93839a2ce2b31b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
您最近一年使用:0次
2020-04-02更新
|
228次组卷
|
4卷引用:学科网3月第一次在线大联考(江苏卷)(理科)
(已下线)学科网3月第一次在线大联考(江苏卷)(理科)(已下线)理科数学-学科网3月第一次在线大联考(江苏卷)文科数学-学科网3月第一次在线大联考(江苏卷)江西省靖安中学2021届高三上学期第四次月考数学(文)试题
12-13高二上·辽宁大连·期末
名校
解题方法
5 . 已知函数
在
上不具有单调性.
(1)求实数
的取值范围;
(2)若
是
的导函数,设
,试证明:对任意两个不相等正数
,不等式
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc4b129481bd8a2fa66f61c3cbb7125a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20251bc82067179f013288b5c338856.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08901950607f256e24e0ab9bf74b1c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff60eab72de85437e12806474281612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a05d8e941031251ba80b00febda3de83.png)
您最近一年使用:0次
2018-01-09更新
|
594次组卷
|
5卷引用:江苏省扬州大学附属中学东部分校2020-2021学年高二下学期第二次模块学习效果调查数学试题
江苏省扬州大学附属中学东部分校2020-2021学年高二下学期第二次模块学习效果调查数学试题(已下线)2011-2012学年辽宁省瓦房店市高级中学高二上学期期末理科数学试卷安徽省淮南市第二中学、宿城第一中学2018届高三第四次考试数学(理)试题海南省海口市第一中学2020届高三9月月考数学试题(A卷)(已下线)2021年高考数学押题预测卷(山东卷)03
名校
解题方法
6 . 已知
(其中
且
,
是自然对数的底).
(1)当
,
时,求函数
在
处的切线方程;
(2)当
时,求函数
在
上的最小值;
(3)若
且关于
的不等式
在
上恒成立,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ad8045fb0d30a5ee6d24aa61f219c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360ff131c51a4ef6745538c18cec92c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4331e1a07b618d102d71dd4943efacff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f2821b63db159c8c94063627747691.png)
您最近一年使用:0次
2020-04-24更新
|
231次组卷
|
2卷引用:江苏省苏州市2018-2019学年高二下学期期末理科数学试题
名校
解题方法
7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
(1)若直线
与
的图象相切,求实数
的值;
(2)设
,讨论曲线
与曲线
公共点的个数;
(3)设
,比较
与
的大小,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6767830cc1811f0f4ea5a008fdc7e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef7ecdafd90c0dc8f2c59194678a97e.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f89a8b5cf6996a6455375e405bfb9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b65c07088cc0800949971c8ce97992.png)
您最近一年使用:0次
8 . 设函数
.
(Ⅰ)求函数
的单调区间;
(Ⅱ)记函数
的最小值为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba5fb7e813068534069ecde66a4f75a.png)
(Ⅰ)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
(Ⅱ)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df08979e3fac3d08f849964e68312f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/543ada8a608820801861f1cb0b78d9e9.png)
您最近一年使用:0次
2018-12-24更新
|
387次组卷
|
5卷引用:江苏省徐州部分学校2024届高三上学期9月期初考试数学试题
9 . (1)证明:当
,
时,有
;
(2)证明:当
,
,且
时,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc01b9e0faacd00ea1201e9f6a9acae3.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cc807f76d58df49f083de0c4a21eff3.png)
您最近一年使用:0次
10 . 已知函数
.
(1)判断
的单调性,并写出单调区间;
(2)若
存在两个零点
,
,求
的取值范围,并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3450b285777d224cef90c0b26a8c6c.png)
(1)判断
![](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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a3ad8c843c361565d0f3cb06da49f60.png)
您最近一年使用:0次
2021-08-11更新
|
164次组卷
|
2卷引用:江苏省南京市六校联合体2020-2021学年高二下学期期末数学试题