1 . 函数
的定义域为D,满足对任意的
,都有
.
(1)若
,试判断
的奇偶性并证明你的结论;
(2)若
,且
在定义域D上是单调函数,满足
,解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d72359aa32e622429742bf70b0064a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836fcad6a6fec95c876177e58d1a916b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05fa0b90dfbce1b77bdd0e2f35c91d1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c8a116f962ae769863da8cf8e8b1b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01ae1955ff955428876290990fe9ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e60ae3f70bd78b0908d480116edefb.png)
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解题方法
2 . (重点班)我们知道对数函数
,对任意
,都有
成立,若
,则当
时,
.参照对数函数的性质,研究下题:定义在
上的函数
对任意
,都有
,并且当且仅当
时,
成立.
(1)设
,求证:
;
(2)设
,若
,比较
与
的大小.
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/b5942922aeb24620a1c49b7605cf0bfb.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/0934a030347c48c3880c29572b64814e.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/2b0a82bdaf4b4268ba7930ead03210c4.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/33b03ed2a5bf44c39bdec82731a58261.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/f6585ab9bcf94bc38252246ae3bc5f15.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/37a99ef913544ae39830cb203c13f4c3.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/67a7718dfb4e493b98483b3d7f231a9d.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/507953f2fdc743a89067d93287d5f8bb.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/71e79fa76ec44c82b2472d7ca54f98dc.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/2b0a82bdaf4b4268ba7930ead03210c4.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/f6585ab9bcf94bc38252246ae3bc5f15.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/37a99ef913544ae39830cb203c13f4c3.png)
(1)设
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/71e79fa76ec44c82b2472d7ca54f98dc.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/ccad5d094f9545dab2cef638fba6b54d.png)
(2)设
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/62f413e2b7714b38a5ca6365eab88291.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/b7f37f360ce1479e88076ccd8f6e9265.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/28e06482f512446c99a3728a6a0ad86e.png)
![](https://img.xkw.com/dksih/QBM/2016/11/7/1573130429054976/1573130435534848/STEM/548602ce8fe74687a860f37a27d686e0.png)
您最近一年使用:0次
2016-12-05更新
|
193次组卷
|
2卷引用:2016-2017学年甘肃武威一中高一上学期阶段考一数学试卷
3 . 设函数
.
(Ⅰ)当
时,讨论函数
的零点个数;
(Ⅱ)若对于给定的实数
,存在实数
,使不等式
对于任意
恒成立.试将最大实数
表示为关于
的函数
,并求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3783882a35084e2031a50508570677e0.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eda48853e8bdb7e266370b4e0d5a258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(Ⅱ)若对于给定的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c6a68c019c7929744be2fc59413db3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://img.xkw.com/dksih/QBM/2015/7/1/1572157961822208/1572157968072704/STEM/873aca0bbb90437793b40749a96d0f3e.png)
![](https://img.xkw.com/dksih/QBM/2015/7/1/1572157961822208/1572157968072704/STEM/acace16481e5405b984dd3008986767e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15234ca1220f277a08ebefa9078986f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15234ca1220f277a08ebefa9078986f.png)
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4 . 设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43d6a1c84ae361dd0f109a2c974988e.png)
(Ⅰ)求
;
(Ⅱ)证明:
在
内有且仅有一个零点(记为
),且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43d6a1c84ae361dd0f109a2c974988e.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2e9b21aafe970e783c5bfa50e0916f.png)
(Ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1bec31a35ce0881c71cb9329805791.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f49736cd096c03dccc9116d4d04906.png)
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2016-12-03更新
|
2286次组卷
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7卷引用:2015年全国普通高等学校招生统一考试文科数学(陕西卷)
2015年全国普通高等学校招生统一考试文科数学(陕西卷)(已下线)专题二 求导法则及复合函数求导-2020-2021学年高中数学专题题型精讲精练(2019人教B版选择性必修第三册)(已下线)6.1.4 求导法则及其应用(课后作业)-2020-2021学年高中数学同步备课学案(2019人教B版选择性必修第三册)(已下线)第六章 导数及其应用 6.1 导数 6.1.4 求导法则及其应用(已下线)专题28 证明不等式的常见技巧-学会解题之高三数学万能解题模板【2022版】(已下线)考点19 导数的应用--函数零点问题 2024届高考数学考点总动员(已下线)专题21 数列解答题(文科)-3
真题
5 . f(x)=x3+2ax2+bx+a,g(x)=x2﹣3x+2,其中x∈R,a、b为常数,已知曲线y=f(x)与y=g(x)在点(2,0)处有相同的切线l.
(Ⅰ) 求a、b的值,并写出切线l的方程;
(Ⅱ)若方程f(x)+g(x)=mx有三个互不相同的实根0、x1、x2,其中x1<x2,且对任意的x∈[x1,x2],f(x)+g(x)<m(x﹣1)恒成立,求实数m的取值范围.
(Ⅰ) 求a、b的值,并写出切线l的方程;
(Ⅱ)若方程f(x)+g(x)=mx有三个互不相同的实根0、x1、x2,其中x1<x2,且对任意的x∈[x1,x2],f(x)+g(x)<m(x﹣1)恒成立,求实数m的取值范围.
您最近一年使用:0次
2016-12-03更新
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2034次组卷
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2卷引用:2011年普通高等学校招生全国统一考试文科数学(湖北卷)