名校
解题方法
1 . 设函数
,其中a为常数.对于给定的一组有序实数
,若对任意
、
,都有
,则称
为
的“和谐数组”.
(1)若
,判断数组
是否为
的“和谐数组”,并说明理由;
(2)若
,求函数
的极值点;
(3)证明:若
为
的“和谐数组”,则对任意
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8beb896a3c01154585e0ec979934f602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911f2e62e650373b98e1b76fb8a8b24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33890c6b0bf167514d44139d9dca0154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774ac39e474f9c5f4e17a4c0416413cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911f2e62e650373b98e1b76fb8a8b24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b6a9ffffc0c461881b427c543924cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e7c12bff76b3a3151dc3e392c60d53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911f2e62e650373b98e1b76fb8a8b24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af0614daffb549e1adc7c24a5bbdf42.png)
您最近一年使用:0次
2023-05-11更新
|
733次组卷
|
5卷引用:上海市七宝中学2023届高三下学期4月月考数学试题
上海市七宝中学2023届高三下学期4月月考数学试题上海市南洋中学2023届高三三模数学试题上海市金山中学2022-2023学年高二下学期期末数学试题上海市静安区风华中学2024届高三上学期10月月考数学试题(已下线)上海市高二数学下学期期末模拟试卷02--高二期末考点大串讲(沪教版2020选修)
名校
2 . 如果曲线
存在相互垂直的两条切线,称函数
是“正交函数”.已知
,设曲线
在点
处的切线为
.
(1)当
时,求实数
的值;
(2)当
,
时,是否存在直线
满足
,且
与曲线
相切?请说明理由;
(3)当
时,如果函数
是“正交函数”,求满足要求的实数
的集合
;若对任意
,曲线
都不存在与
垂直的切线
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749c140afe3f0d42e3cad85909d63938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06dfc9e95cade14ae9b7fc89519a2dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedde86fd5b5e93c14ffd9190fc7d7a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cfc27d13b4d07ade4729b481cc95735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/534180efa9c8ffc5ac7cf7f2f035d11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4526d19896bdff6cb66b4aea9a6ef24d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24600bfcfb91c661eb9d237956e011ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
2023-04-14更新
|
977次组卷
|
5卷引用:上海市闵行区2023届高三二模数学试题
上海市闵行区2023届高三二模数学试题(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)专题08 平面解析几何-学易金卷湖北省襄阳市第五中学2023届高三下学期适应性考试(一)数学试题
3 . 某小区有块绿地,绿地的平面图大致如下图所示,并铺设了部分人行通道.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/c506cd7e-0c97-49b3-acfb-a25b782ba60b.png?resizew=168)
为了简单起见,现作如下假设:
假设1:绿地是由线段
,
,
,
和弧
围成的,其中
是以
点为圆心,圆心角为
的扇形的弧,见图1;
假设2:线段
,
,
,
所在的路行人是可通行的,圆弧
暂时未修路;
假设3:路的宽度在这里暂时不考虑;
假设4:路用线段或圆弧表示,休息亭用点表示.
图1-图3中的相关边、角满足以下条件:
直线
与
的交点是
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fdb2b9d6a4a54ed1328c5b3adcf7b6.png)
,
.
米.
小区物业根据居民需求,决定在绿地修建一个休息亭.根据不同的设计方案解决相应问题,结果精确到米.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/15/5e27693b-d213-4a76-b176-210f478b2a83.png?resizew=565)
(1)假设休息亭建在弧
的中点,记为
,沿
和线段
修路,如图2所示.求
的长;
(2)假设休息亭建在弧
上的某个位置,记为
,作
交
于
,作
交
于
.沿
、线段
和线段
修路,如图3所示.求修建的总路长
的最小值;
(3)请你对(1)和(2)涉及到的两种设计方案做个简明扼要的评价.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/c506cd7e-0c97-49b3-acfb-a25b782ba60b.png?resizew=168)
为了简单起见,现作如下假设:
假设1:绿地是由线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0450d195423158b2963b517f0425ba57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0450d195423158b2963b517f0425ba57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
假设2:线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0450d195423158b2963b517f0425ba57.png)
假设3:路的宽度在这里暂时不考虑;
假设4:路用线段或圆弧表示,休息亭用点表示.
图1-图3中的相关边、角满足以下条件:
直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fdb2b9d6a4a54ed1328c5b3adcf7b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c4340dcffb0783d118a587e5352a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79f2eff72d0b77615ee85ec9676a8d16.png)
小区物业根据居民需求,决定在绿地修建一个休息亭.根据不同的设计方案解决相应问题,结果精确到米.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/15/5e27693b-d213-4a76-b176-210f478b2a83.png?resizew=565)
(1)假设休息亭建在弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0450d195423158b2963b517f0425ba57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0450d195423158b2963b517f0425ba57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350e954f629c1901a5cec03558319e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350e954f629c1901a5cec03558319e46.png)
(2)假设休息亭建在弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0450d195423158b2963b517f0425ba57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a470095e295c734a2f368cc6baf1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd378d3805a3d8295aec88bf3684f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a4fdec4ee1fc83fdd6b4c324755d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66f7735b5a72e63461fbf457e7e3977.png)
(3)请你对(1)和(2)涉及到的两种设计方案做个简明扼要的评价.
您最近一年使用:0次
2023-04-13更新
|
538次组卷
|
4卷引用:上海市闵行区上海外国语大学闵行外国语中学2024届高三上学期期中数学试题
名校
解题方法
4 . 已知无穷数列A:
,
,…满足:①
,
,…
且
;②
,设
为
所能取到的最大值,并记数列
:
,
,….
(1)若数列A为等差数列且
,求其公差d;
(2)若
,求
的值;
(3)若
,
,求数列
的前100项和.
![](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/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df437d00ab1fd773e9d8d8f378455f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a49997086be2e13a271a4a7b1d4c399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f63f64193d72aca5e88a2ea51e5ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d00457e8d086f28ea1b24bd880c9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f766f204cf98d973ad5abe03b235e95a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6398ba56f5a708d2d85a02320e1a389d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8c641c42b6cd7f44c477bbe5761a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7488ed7332650aa2bc908edbd38c05e8.png)
(1)若数列A为等差数列且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7104dd8a81267b6c15ceedcefccfa20.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6398ba56f5a708d2d85a02320e1a389d.png)
您最近一年使用:0次
2023-04-02更新
|
647次组卷
|
4卷引用:上海交通大学附属中学闵行分校2022-2023学年高二下学期3月月考数学试题
上海交通大学附属中学闵行分校2022-2023学年高二下学期3月月考数学试题上海市交通大学附属中学2022-2023学年高二下学期3月卓越考试数学试题江苏省南京市2024届高三上学期零模考前押题数学试题(已下线)4.4 数学归纳法(五大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
22-23高二下·上海浦东新·阶段练习
名校
5 . 已知函数
,其中b,d为常数,函数
是其导函数,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c2230765577633894801bf0b9162bb.png)
(1)求函数
的解析式;
(2)若函数
在某点处的切线过点
,求切线的一般式方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eabb34b4fb727011fcd216e718f52703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c2230765577633894801bf0b9162bb.png)
(1)求函数
![](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/ceb33149b06f538ebff0442560ca7df9.png)
您最近一年使用:0次
6 . 设函数
,其中
.
(1)当
时,求函数
在
处的切线方程;
(2)讨论
的单调性;
(3)若
的图象与
轴没有公共点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4054c4a83bdb2de96890bd62e6702bf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e88ebfb5c0d6cce558b515be06404d.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
7 . 对任意实数
,记
为不大于
的最大整数,再记
,由此可定义函数
,进而可定义递推数列
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/73191ebb-ef41-4fb1-8007-e0091a02c77e.png?resizew=231)
(1)求
的定义域,并判断
是否有反函数(只需写出判断结果,无需说明理由).
(2)求证:①
的每一项都是正有理数;②
的任意两项均不同.
(3)为进一步研究
各项的取值情况,有人把该数列排成了下述的“二分树状表”,并探究了图中由箭头连接的两数间的关系,进而猜想“
的各项取遍所有正有理数”.请你判断该猜想是否正确,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7db6fc42e0baf315ff7c5a30ff8ba73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb43db0a1162d7407114fb7efc74b79e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e121e47d3b2f0dc79f008fa9f215f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af3867356b63012dba362fa7267a333.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/73191ebb-ef41-4fb1-8007-e0091a02c77e.png?resizew=231)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求证:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)为进一步研究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
名校
8 . 已知函数
,
.
(1)判断函数
的奇偶性;
(2)若函数
在
处有极值,且关于x的方程
有3个不同的实根,求实数m的取值范围;
(3)记
(
是自然对数的底数).若对任意
、
且
时,均有
成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912a45855a0231c91bc3b9f9ecceb816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43fb7af688c7d890a2221ab00eee4e54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8463f441f99b82fa2f315b39baa25a4.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd95de578b27d676f4e9ac3db58af675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9355f07b98a27884fb028fef70e72df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2210f152080d9a68a97c805f5c1cde96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191a9f1cd3402de148664b7fbe7a0c79.png)
您最近一年使用:0次
2022-12-16更新
|
1473次组卷
|
10卷引用:上海市莘庄中学2022-2023学年高二下学期期中数学试题
上海市莘庄中学2022-2023学年高二下学期期中数学试题上海市宝山区2023届高三上学期一模数学试题上海市位育中学2023届高三下5月高考模拟数学试题上海市南洋模范中学2024届高三上学期开学考试数学试题(已下线)第六章 导数与不等式恒成立问题 专题九 双变量不等式恒成立问题 微点1 值域法破解双变量不等式恒成立问题上海市浦东新区浦东中学2024届高三上学期期中数学试题2024届上海市闵行(文绮)中学高考三模测试数学试卷上海市行知中学2023-2024学年高二下学期3月考试数学试卷(已下线)专题05导数及其应用--高二期末考点大串讲(沪教版2020选修)(已下线)上海市高二下学期期末真题必刷03(常考题)--高二期末考点大串讲(沪教版2020选修)
名校
9 . 若函数
在定义域内给定区间
上存在
(
),满足
,则称函数
是区间
上的“平均值函数”,
是它的平均值点.
(1)已知函数
是区间
的“平均值函数”,求该函数的平均值点;
(2)当函数
是区间
上的“平均值函数”,且有两个不同的平均值点时,求实数
的取值范围;
(3)是否存在区间
(
),使得函数
是区间
上的“平均值函数”?若存在,求出所有满足条件的区间
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2a6fa3bc621d26261cf595a5802a3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7c63ce0b2b86b4706c1f853b0e5e8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9e6f14c8fe38f0e18007a60144fd55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a92ba8b43bebdf7d6c40917f4d3e110.png)
(2)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4299d08471f0e3d0ef6448b97b11713f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)是否存在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a72029d2a0763cce946eeca632a6c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
您最近一年使用:0次
2022-11-17更新
|
855次组卷
|
4卷引用:上海市闵行(文绮)中学2023届高三下学期开学学情调研数学试题
上海市闵行(文绮)中学2023届高三下学期开学学情调研数学试题(已下线)2023年四省联考变试题17-22上海市奉贤区奉贤中学2023届高三上学期期中数学试题上海市金山中学2023届高三上学期期中数学试题
名校
10 . 已知函数
.
(1)求函数
在
处切线方程;
(2)若对任意的
,
恒成立,求
的取值范围;
(3)当
时,设函数
,对于任意的
,试确定函数的零点个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79e53eb045a1368e2c2513dca431467.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb29b273ea2b765519835eef9faac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ce93b9f0ea8d7e3a5e4a4f2fcacf45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2817c52144d06555e98131b5e657c4.png)
您最近一年使用:0次
2022-08-23更新
|
755次组卷
|
7卷引用:上海市闵行中学2024届高三上学期开学考试数学试题
上海市闵行中学2024届高三上学期开学考试数学试题上海市宜川中学2024届高三上学期10月月考数学试题上海市回民中学2024届高三上学期期中数学试题上海市控江中学2021-2022学年高二下学期期末数学试题上海市洋泾中学2023届高三上学期开学考试数学试题(已下线)第21讲 导数的八种解题模型-2(已下线)高二上学期期末【压轴60题考点专练】(选修一+选修二)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)