名校
1 . 已知函数
,函数
.
(1)求函数
在
处的切线方程;
(2)当
时,证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b6ac28c5d47676114c28c804840c16.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966b60302d80d8613675bb3dd5c03164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561800aa679a45da4dbe0e323de1fd59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f94150c2d9a4d142228619ae4c5b32a.png)
您最近一年使用:0次
2020-12-22更新
|
187次组卷
|
2卷引用:江苏省南通市海门中学2020-2021学年高三上学期阶段检测(二)数学试题
名校
解题方法
2 . 已知函数
在
处的切线方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ec60c1d5e99c7dd9d343f0127bff95.png)
(1).求
的解析式;
(2).若对任意的
,均有
求实数k的范围;
(3).设
为两个正数,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f89d1045355084403aa3c3bfe812a4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187c21027ff08411931d32c530b64fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ec60c1d5e99c7dd9d343f0127bff95.png)
(1).求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2).若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147ed879fbe216a902b729fcbe96b981.png)
(3).设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8ca3aa2d1ba52e82613d0d65d800e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36af67dca04ff106d65a4a3505acb224.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
,
.
(1)若函数
在其定义域内为单调减函数,求a的取值范围;
(2)若函数
的图像在x=1处的切线斜率为0,且
,证明:对任意的正整数n,当
时,
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36677679bef51ee6028252bcac01a89c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3471484b64504fc545398f52be830010.png)
(1)若函数
![](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/66fe7e0b717e3fc1771652a8afc80115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0175a04676b1448f86f6fdb5204ff7b4.png)
您最近一年使用:0次
解题方法
4 . 已知函数
的最小值为
.
(1)设
,求证:
在
上单调递增;
(2)求证:
;
(3)求函数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3697d8321318c0ea408bbf340055dc9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585de67a3fc494297d375d339af6d153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d7a485fbf1d06e4ce1d06b15c78b703.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75f9ce5eadb0f4dabe90388ce52b3fc.png)
您最近一年使用:0次
2018-01-19更新
|
494次组卷
|
2卷引用:江苏省泰州市2017~2018学年度高二第一学期期末考试数学(理科)试题
解题方法
5 . 已知函数
,函数
,函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608da5b8b969a1824732444e1bffe28e.png)
(1)当函数
在
时为减函数,求a的范围;
(2)若a=e(e为自然对数的底数);
①求函数g(x)的单调区间;
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44631a5498ac443217d8f00a5efab7a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3b0de07ca24df1fcd0a4c49ccc91f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608da5b8b969a1824732444e1bffe28e.png)
(1)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dafea184dce8d6fdcf0297f7fd9d7444.png)
(2)若a=e(e为自然对数的底数);
①求函数g(x)的单调区间;
②证明:
![](https://img.xkw.com/dksih/QBM/2015/6/25/1572146522185728/1572146528198656/STEM/9958286643ea4471a7fdb5a5a1f7f355.png)
您最近一年使用:0次
2016-12-03更新
|
833次组卷
|
4卷引用:2015届江苏高考南通密卷六数学试卷
2015届江苏高考南通密卷六数学试卷江苏省合作联盟学校2019-2020学年高三下学期阶段性调研测试数学试题2020届江苏省合作联盟学校高三下学期4月模拟数学试题(已下线)预测02 函数与导数-【临门一脚】2020年高考数学三轮冲刺过关(江苏专用)
解题方法
6 . 已知函数
.
(1)
时,求
的零点个数;
(2)若
恒成立,求实数
的最大值;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf8a50553b1b9040eb5fd8149602f0b.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3c2be7482719651bcf491949681e05.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e7c3a84d5c3ab338a6b95d1e4a7ce8a.png)
您最近一年使用:0次
名校
解题方法
7 . 记
.
(1)若
,求证:
对任意的
恒成立;
(2)若直线l:
与
的图象相切于点
.
①试用m表示a与k;
②若k为常数且
),求证:总存在三个不同的实数
,
,
,使得直线l与曲线
,
,
同时相切.(参考数据:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0eb761a1b7926f785748bbf588a39c8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc28726e303fa2a5ca1c5d74926bbfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
(2)若直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6767830cc1811f0f4ea5a008fdc7e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c98d225870c139808946d726257ba89f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c846ac5f5576ebb3fb28bba8012f390.png)
①试用m表示a与k;
②若k为常数且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b9f5d64488ad09204340f10d3cf04d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c488de3215dee319cd0cf0badbde4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f88316a636b6a0acdfec4cdab77c9d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800ff501f29a965c4c9dac88263ca2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7739fabf233e5b2136faf751a7ebc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7344b05293a5dfd7d6d199763cf9b3.png)
您最近一年使用:0次
2011·江苏·一模
解题方法
8 . 已知函数
,
,
,
.
(1)求函数
在点
处的切线方程;
(2)若
在区间
上恒成立,求
的取值范围;
(3)当
时,求证:在区间
上,满足
恒成立的函数
有无穷多个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bfecd54416e2e0366376999e752915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a2216be8742c0fcd67c8185a255aa7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7c6915d8302ea5c84ed1d5e14ef42e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c4f8e8106a49b3a3b60810076989dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51947e18ac12b186aa3c09e62c036af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc40a37a51ff1dbff3bf0ff2e0adf7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
名校
9 . 已知函数
(
)有两个零点
,
,且
.
(1)求a的取值范围:
(2)设函数
的极值点为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2bcab5acda7636a9ee4be9808a7135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.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/26d8dafc71b106f39f4e15442220897b.png)
(1)求a的取值范围:
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c4731f09a45182572b481d3ca6c33b.png)
您最近一年使用:0次
10 . 对于函数
与
,若存在实数
满足
,且
,则称
为
的一个
点.
(1)证明:函数
与
不存在
的
点;
(2)若函数
与
存在
的
点
,求
的范围;
(3)已知函数
,证明:存在正实数
,对于区间
内任意一个
皆是函数
的
点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192ded2afcb5ac2f498ad84ebfd91d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd4e5e2e8ee788de9c2f5e34b3a5650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d0d2a14ac5374fe31c385a8cd1336f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d5764793c323fe28c585b8b4af5a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892f97ad8b85728f98958d0bf5e6f4b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054775ba84117cafcf511ca8eeb5cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914a49b0d7aedc593a3e87fbab7c31ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8e298ed59fae5ab49e65df71107d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58164fe4f05f14c63dee4419f3baf969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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