名校
解题方法
1 . 三个互不相同的函数
与
在区间
上恒有
或恒有
,则称
为
与
在区间
上的“分割函数”.
(1)设
,试分别判断
是否是
与
在区间
上的“分割函数”,请说明理由;
(2)求所有的二次函数
(用
表示
,使得该函数是
与
在区间
上的“分割函数”;
(3)若
,且存在实数
,使得
为
与
在区间
上的“分割函数”,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7389d52e6aad9c9c0fb7d9b820bdb86c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212983432fdb9bb12719fc9be4b410d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d61157daf46974d1a08cd4b465a92abe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf539cf2851e1fbaf08845506a069819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e0e7bfdc55e8a26a7db4952d9ccc5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a05ba1bc6c7bc24879b2a17ef2351c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572f286fb45b2757af63569ae0bc2e99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2372f424431ce7b547a66b7d61d75421.png)
(2)求所有的二次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154b365001d4d23ea096b4a55ad42ae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca8b76236aa2fcdd30d2f1915f0c748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a05ba1bc6c7bc24879b2a17ef2351c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23afc43a8c5b8cfe6bf2a1caed920c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2372f424431ce7b547a66b7d61d75421.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a06e1578853d2072cef33395de8784d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceee0ff5c929d67de3c294e027c9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aea89f800e9af713ec91e00fb287008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ed21127710fb6adcf694bd14aff321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
您最近一年使用:0次
2023-04-13更新
|
977次组卷
|
5卷引用:重难点04导数的应用六种解法(1)
(已下线)重难点04导数的应用六种解法(1)(已下线)第5章 函数的概念、性质及应用单元复习+热考题型-同步精品课堂(沪教版2020必修第一册)上海市黄浦区2023届高三二模数学试题河北省衡水中学2023届高三下学期第五次综合素养测评数学试题上海市市北中学2024届高三上学期10月月考数学试题
名校
2 . 已知
,等差数列
的前
项和为
,记
.
(1)求证:函数
的图像关于点
中心对称;
(2)若
、
、
是某三角形的三个内角,求
的取值范围;
(3)若
,求证:
.反之是否成立?并请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71de2abab31c4eb56f306f90dab97b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5395b2d08fce7c50d6281ef406cfe4bf.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd4b78b52a322453c700b62660e6ca57.png)
(2)若
![](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/155c5f3a5c55e0c95191c5a893f63062.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4847cf7c0d99d9c83ca571bef8eefc9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58b9a59084755c0a4781922cfa03ee5.png)
您最近一年使用:0次
2023-04-13更新
|
1050次组卷
|
3卷引用:专题06 数列及其应用
名校
解题方法
3 . 设
是定义域为
的函数,当
时,
.
(1)已知
在区间
上严格增,且对任意
,有
,证明:函数
在区间
上是严格增函数;
(2)已知
,且对任意
,当
时,有
,若当
时,函数
取得极值,求实数
的值;
(3)已知
,且对任意
,当
时,有
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a58786946f71a4cca026b03209f077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a75ad60c144a70f02452336fbfe706b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b98756428d4570b72d0286cb2dc209.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d71122e87403561adbcdac88945c481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dffc6b2381466e8c5e9d63662d4e5c50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2440f783ad81b8da348c4ce89c8149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b161d1fa052b4b7b1d991da282b6bf84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a75ad60c144a70f02452336fbfe706b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dffc6b2381466e8c5e9d63662d4e5c50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75965da655669b120d5f28c4247b7bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5223ece2f8f76850c49e2505304532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a75ad60c144a70f02452336fbfe706b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f08e4ae2ae9dfb90daf707cb5578c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
您最近一年使用:0次
2023-04-12更新
|
1000次组卷
|
7卷引用:专题03 导数及其应用
(已下线)专题03 导数及其应用(已下线)专题02 函数及其应用(已下线)重难点04导数的应用六种解法(1)上海市青浦区2023届高三二模数学试题上海市北蔡中学2023-2024学年高二上学期12月月考数学试卷(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编湖南省株洲市第二中学2023-2024学年高三下学期开学考试数学试卷
解题方法
4 . 已知定义在
上且不恒为
的函数
,若对任意的
,都有
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64541d7f445079207b6f671adc7d662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/649df22b06d6aa4123fcbbba8e759532.png)
A.函数![]() |
B.对![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
解题方法
5 . 给出下列说法,其中正确的是( )
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
您最近一年使用:0次
2023-04-09更新
|
1452次组卷
|
4卷引用:第二章 函数的概念与性质 第二节 函数的单调性与最值(讲)
(已下线)第二章 函数的概念与性质 第二节 函数的单调性与最值(讲)山西省部分学校2023届高三下学期4月联考数学试题辽宁省县级重点高中联合体2023届高三二模数学试题吉林省白山市2023届高三下学期四模联考(4月期中)数学试题
名校
解题方法
6 . 已知
是
上的偶函数,且当
时,
.若
, 则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94b194a693b296656b887a148fd2266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8e7413ac3019f5e06f978b1550fe33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1810427271c91b1527d0a2f5ec46bcb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca3ecbbaca8eeb1cfa8f4035f7d5726.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-04-08更新
|
1346次组卷
|
6卷引用:押新高考第8题 函数的基本性质
名校
解题方法
7 . 已知函数
在
上单调递减,在
上单调递增.记函数
.
(1)写出函数
的单调区间(无需说明理由)及其最小值;
(2)若直线
与函数
和
的图象共有三个不同的交点,从左到右依次记为
,
,
,试证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2399c2a712a2890dcd0b195d3b9f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6097169b69ad927c38efd7d52ec65f95.png)
(1)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af79f45b5880c72a349500da9d8e118d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c16dac1e9bf5804c8907cbc59014d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6fbfe23e06cc72f33f925dd5ee3351e.png)
您最近一年使用:0次
解题方法
8 . 已知
,设
,
是函数
与
图象的两个公共点,记
.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf5b71b934df1f12d4755c9551517bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3ba93565b37938db0d2f302ebd452d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0b0d73b90f97765c90bb9bec1a6d7b.png)
A.函数![]() ![]() | B.函数![]() ![]() |
C.函数![]() | D.函数![]() |
您最近一年使用:0次
9 . 已知定义域为D的函数
,其导函数为
,满足对任意的
都有
.
(1)若
,
,求实数a的取值范围;
(2)证明:方程
至多只有一个实根;
(3)若
,
是周期为2的周期函数,证明:对任意的实数
,
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68a65126b7e2d009d067f80c34f939d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb510f17d7fa00d07caf7391253b8c67.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b8a5b607b38ac9ba7c18468d07b155.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
(2)证明:方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54ce1d0d23531eba7c795b2f53a5b280.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29aef458f2367b76432719f6f56275d8.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/9b1ab2e5e3dd3a1c768a88eb182b44d9.png)
您最近一年使用:0次
名校
10 . 定义:对于定义在区间
上的函数
和正数
,若存在正数
,使得不等式
对任意
恒成立,则称函数
在区间
上满足
阶李普希兹条件,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79855073207c4af3392f757357e348cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02fb9bc8880f31122bf58269d720bf6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243a45670e2b2fe44496d3244ed5a68d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.函数![]() ![]() ![]() |
B.若函数![]() ![]() ![]() |
C.若函数![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.若函数![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-04-08更新
|
2937次组卷
|
11卷引用:专题05导数及其应用(选择题)
专题05导数及其应用(选择题)(已下线)模块六 专题1 易错题目重组卷(河北卷)(已下线)数学(云南,安徽,黑龙江,山西,吉林五省新高考专用)(已下线)山东省实验中学2024届高三第一次诊断考试数学试题变式题11-14河北省石家庄市2023届高三教学质量检测(二)(一模)数学试题河北省邢台市2023届高三下学期4月联考(一模)数学试题湖南省长沙市第一中学2023届高三一模数学试题河北省秦皇岛市第一中学2023届高三二模数学试题河南省许昌市禹州市高级中学2023-2024学年高三上学期11月月考数学试题(已下线)专题23 导数及其应用小题(已下线)专题8 函数新定义问题(过关集训)(压轴题大全)