12-13高二上·辽宁大连·期末
名校
解题方法
1 . 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
2 . 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
3 . 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
4 . 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
2011·江苏南京·一模
解题方法
5 . 已知函数
,
的导数是
.
(1)求
时,
在
处的切线方程;
(2)当
时,求证:对于任意的两个不等的正数
,有
;
(3)对于任意的两个不等的正数
,若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6e0aa9cdd53246f9fdf6b419ed3046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e808873b814cf720131eeed83e88bf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.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/842c7c006e7972a694a8ba7967375b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb572cf70a40f65fb90f3e93cdc439b.png)
(3)对于任意的两个不等的正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd0d39581d8ef68a81fdff4f2a06b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
6 . (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
解题方法
7 . 已知函数
,
.
(1)当
时,求函数
的单调区间;
(2)若不等式
对任意的正实数
都成立,求实数
的最大整数值.
(3)当
时,若存在实数
且
,使得
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51b45c6ae148fd6ee91b3cd79050726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e0cdbc2165b9a3477b6ffe4057f699.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acda6b6464db27e1ec18a1522406d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1f72c12b33e1f8a8669c8064aacd71b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87027136ff548fc504dea240e75cea86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9ba50ede8ef97b843accf839fef5c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924e707a7e33bfcccbc05c8c5557a0af.png)
您最近一年使用:0次
8 . 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
解题方法
9 . 设函数
.
(1)若函数
是R上的单调函数,求实数
的取值范围;
(2)设
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/458b4b6612ec377f7cb9687c11000796.png)
,
是
的导函数.
①若对任意的
,求证:存在
,使
;
②若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4690e9a7ab759e1ad5c1fc6f13485cf.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/458b4b6612ec377f7cb9687c11000796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42b1d90a95e6795fa3f6037553e83e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
①若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd393638255ec3652ef6dd80415c03e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6bfaaac40689ea19291d831097c2b8.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfb4ecfcd09ce9d668607c2f209238c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba56f8b70d256d9c278adc2de0548a78.png)
您最近一年使用:0次
2018-04-04更新
|
609次组卷
|
2卷引用:江苏省苏北六市2018届高三第二次调研测试数学(文科)试题
名校
10 . 已知函数
,函数
的导函数为
.
(1)若直线
与曲线
恒相切于同一定点,求
的方程;
(2)若
,求证:当
时,
恒成立;
(3)若当
时,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2c8724cd02ac98c8b579601799c07c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f88a76f947e7022ef0c5efd6db060c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32253cf35c200300131537065498f088.png)
(3)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48c2fef1fea8cb5065e9255bc08a6bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2017-11-20更新
|
879次组卷
|
2卷引用:江苏省常州市武进区2018届高三上学期期中考试数学(文)试题