解题方法
1 . 已知
的定义域为
,且
,且
.
(1)证明
是偶函数;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f6cd8b41d4d12a06a4e84e8c0f0900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ef022cb5ccd3757adda282dccca52b.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c97cdbb3ad27a555f765ccb2436bf9.png)
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2 . 对于三次函数
,定义:设
是函数
的导函数
的导数,若
有实数解
,则称点
为函数
的“拐点”.现已知
.请解答下列问题:
(1)求函数
的“拐点”A的坐标;
(2)求证:
的图像关于“拐点”A对称,并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75044e0301ef9def5c1a1c8e6f2cba77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47db775f5675cd10012f964a336832f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4a5292f6af433342a866336d05fe5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de68bc1a57041a038aea6711c8848999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4724249ffd113d05e9a1806c90647e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44497598c08c9e219a7737af9faa1d87.png)
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2022-09-30更新
|
520次组卷
|
6卷引用:1.2.2 函数的和差积商求导法则(同步练习)2022-2023学年高二选择性必修第二册素养提升检测(提高篇)
(已下线)1.2.2 函数的和差积商求导法则(同步练习)2022-2023学年高二选择性必修第二册素养提升检测(提高篇)(已下线)5.2 导数的运算(2)(已下线)第01讲 导数的概念与运算-【寒假预科讲义】2024年高二数学寒假精品课(人教A版2019)(已下线)2023-2024学年高二下学期第一次月考解答题压轴题十六大题型专练(1)河南省南阳市第一中学校2022-2023学年高三上学期第二次阶段考试文科数学试题山西省晋中市平遥县第二中学校2023届高三上学期10月月考数学试题
3 . 根据人教2019版必修一P87页的13题介绍: 函数
的图象关于点
成中心对称图形的充要条件是函数
为奇函数.
题:设函数
,且
, (其中
是常数), 函数
.
(1)求
的值, 并证明
是中心对称函数;
(2)是否存在点
,使得过点
的直线若能与函数
围成两个封闭图形,则这两个封闭图形的面积总相等?若存在,求出点
的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827539d066d1b78e7ef8bc1569864971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d0969cb7acbeaa05a101a385348a00.png)
题:设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da37c944818d98398cb8a08b07a5a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f36aee2bc2bf762d52f7921d58701f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc63be9ab062dcc648ba88568b7269d8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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2022-03-28更新
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472次组卷
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3卷引用:4.1.2 无理数指数幂及其运算性质练习
4 . 函数
.
(1)证明
;
(2)画出函数
的图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4375cccfd9f70b84132c587580198b6c.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b3b657ebd1733b4f19dcbec44919924.png)
(2)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49126fe447c6fa013e03ce3d85dd483c.png)
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名校
解题方法
5 . 定义
是
的导函数
的导函数,若方程
有实数解
,则称点
为函数
的“拐点”.可以证明,任意三次函数
都有“拐点”和对称中心,且“拐点”就是其对称中心,请你根据这一结论判断,以下命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d31f9ce464f2ce3b24833b70595941c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc581690f1d82133bb5fed3d7f365f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75044e0301ef9def5c1a1c8e6f2cba77.png)
A.存在有两个及两个以上对称中心的三次函数 |
B.函数![]() |
C.存在三次函数![]() ![]() ![]() ![]() ![]() |
D.若函数![]() ![]() |
您最近一年使用:0次
2021-07-29更新
|
401次组卷
|
2卷引用:湖北省武汉市江夏一中2020-2021学年高二下学期期中模拟数学试题
解题方法
6 . 已知定义在
上的二次函数
,且
在
上的最小值是8.
(1)求实数
的值;
(2)设函数
,若方程
在
上的两个不等实根为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c009c79f5a2e63c0c06f6d61d70352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf9d86203ddeaab06bdd2f634f1538dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2401f1358466ad761052b98564ae5873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c6ffa6fe2387ee19234c2ad0fcb92ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2d40035607cb9eb4ba2def79d08f0d.png)
您最近一年使用:0次
2020-03-11更新
|
728次组卷
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2卷引用:山东省2017年冬季普通高中学业水平考试数学试题
7 . 现有结论:对于函数
,若对任意
,
,
,则
的图象关于点
中心对称,关于直线
轴对称.
(Ⅰ)利用上述结论,证明函数
的图象关于点
中心对称,关于直线
轴对称.设点
到直线
的距离为
,给出函数
的最小正周期
与
的关系式.
(Ⅱ)若函数
的图象关于点
中心对称,关于直线
轴对称,其中
,猜想:函数
是否为周期函数?如果是,用
表示周期
并证明,如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f1a3feca6218955446108ebad0a524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90f5368e9fcb727db0cba276cc3a840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f493fd8c35b26a218045a0c8a6a5d8c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3e599d2172afd34cefafacc0904bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae52fec0134afc670aed78812818bd3.png)
(Ⅰ)利用上述结论,证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaf693219fef9a0e643cd8d01135b20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968a4125d82dc0d0574c7164fc8f5098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe26258d45da6df1e1d94d9645e3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaf693219fef9a0e643cd8d01135b20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(Ⅱ)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3e599d2172afd34cefafacc0904bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae52fec0134afc670aed78812818bd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d499e8ca8a0c2c810507e34456181577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15bd315b801f71bc30b8d772098614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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8 . 已知函数
的图象过原点,且关于点
成中心对称.
(1)求函数
的解析式;
(2)若数列
满足
,
,试证明数列
为等比数列,并求出数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc88563f9af5bdf8d89c5403449d90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f13464ef59677ed7d9e6de377a2b9254.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663bbc5767b9cb453cb08e1f0a8e0602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb785daec81769811c358049364376d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075505f0a38c393a2bab766cab54c6e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
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9 . 对于函数
,设
是函数
的导数,
是
的导数,若方程
有实数解
,则称点
为函数
的“拐点”.
(1)证明:三次函数的拐点是其图像的对称中心(提示:可将函数
化为
的形式)
;
(2)若设
,计算
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7ec5a0b4f655a796acdd1cb79d32ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604d4be927e22330147c4763c7aaa869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17023464fee468007568c5934550b6a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604d4be927e22330147c4763c7aaa869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ee8b77ea7e26e1fa0b8267877dc70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8dd9094f6f8fca2cc17a4f5c685975f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
(1)证明:三次函数的拐点是其图像的对称中心(提示:可将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a88d36334af006b216e6c3fdad1d2e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2480adfeab8fd25b15fe99ec6b28b6.png)
;
(2)若设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f1944d2ca95fec50a853ff0e9e3853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1b38857ffd824a5d43b268554f93d5.png)
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