1 . 设
是直角坐标平面
上的一点,曲线
是函数
的图象.若过点
恰能作曲线
的
条切线
,则称
是函数
的“
度点”.
(1)判断点
是否为函数
的
度点,并说明理由;
(2)若点
是
的
度点,求
的最小值;
(3)求函数
的全体
度点构成的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067ea3d2afb15333c289187e3c9f3261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)判断点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1a9821a00b71f6b7d7a76d91b3f810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48890339cc88c8dd3c58754739688e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af5cfdc65e6473a2648da0083241912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0660d4864c16652a6b27337462b3f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
,
,令![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375188c08625c1198d55e189de16aa7e.png)
(1)当
时,求函数
在
处的切线方程;
(2)当a为正数且
时,
,求a的最小值;
(3)若
对一切
都成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c12b64c84b3bef41942a5a4f2409799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d89c293b2a43612f08d290746d0925a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375188c08625c1198d55e189de16aa7e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)当a为正数且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d967d4ec242cd32654fc5f96e72d5dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d94a7a0f5a35a8a19d3e003a7f58ba.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d70309304e6f4a34f8efa9b244a05de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8654e969a9b848729a9f2d4fee437606.png)
您最近一年使用:0次
2024-03-07更新
|
1735次组卷
|
13卷引用:上海市实验学校2022-2023学年高三下学期3月月考数学试题
上海市实验学校2022-2023学年高三下学期3月月考数学试题上海市同济大学第一附属中学2023届高三三模数学试题上海市青浦区2022-2023学年高二下学期期末数学试题(已下线)重难点04导数的应用六种解法(1)上海市同济大学第一附属中学2023届高三下学期5月月考(质控2)数学试题上海市风华中学2024届高三上学期期中数学试题上海市浦东新区上海中学东校2024届高三上学期期中数学试题(已下线)模块八 专题11 以函数与导数为背景的压轴解答题上海市上海师范大学附属中学2023-2024学年高三下学期3月月考数学试卷上海市浦东新区上海师大附中2024届高三下学期3月模拟考试数学试题上海市育才中学2024届高三下学期第一次调研(3月)数学试题上海市嘉定区育才中学2024届高三下学期(3月份)一调数学试卷江苏省无锡市江阴长泾中学2023-2024学年高二下学期3月阶段性检测数学试卷
3 . 对于函数
,分别在
处作函数
的切线,记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”,同理记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”
(1)设函数
,记
“切线-
轴数列”为
,记
为
的前n项和,求
.
(2)设函数
,记
“切线-
轴数列”为
,猜想
的通项公式并证明你的结论.
(3)设复数
均为不为0的实数,记
为
的共轭复数,设
,记
“切线-
轴数列”为
,求证:对于任意的不为0的实数
,总有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ed953d6e0bd80a5da66552c7bfbcbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3d48fa9493a86f262569df235a82ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8292395dc894796602a60486e575a808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79b9eaa5e7ab7a1e5c512b571914dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ef5756fec38d1b4dc62358b45c3352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e845964df4b271bd7b4cf99ede79be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(3)设复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bcf306a6aa8554d1d7fc8317f4e946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5f303f666e164582da05968d9d8cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6f044a9b06a7a769e613c977cbfb87.png)
您最近一年使用:0次
2024-01-01更新
|
435次组卷
|
7卷引用:上海市普陀区桃浦中学2022-2023学年高二下学期期中数学试题
上海市普陀区桃浦中学2022-2023学年高二下学期期中数学试题(已下线)模块一专题1【练】《导数的概念、运算及其几何意义》单元检测篇B提升卷(人教A2019版)(已下线)模块二 专题1 与曲线的切线相关问题(已下线)模块二 专题3 与曲线的切线相关问题(人教B版)(已下线)模块一 专题1 《导数的概念、运算及其几何意义》B提升卷(苏教版)(已下线)模块二 专题1 与曲线的切线相关问题(苏教版高二)(已下线)模块二 专题4 与曲线的切线相关问题(高二北师大版)
名校
4 . 已知函数
.
(1)若
,求
的单调区间;
(2)若
时
恒成立,求实数a的取值范围.
(3)定义函数
,对于数列
,若
,则称
为函数
的“生成数列”,
为函数
的一个“源数列”.
①已知
为函数
的“源数列”,求证:对任意正整数
,均有
;
②已知
为函数
的“生成数列”,
为函数
的“源数列”,
与
的公共项按从小到大的顺序构成数列
,试问在数列
中是否存在连续三项构成等比数列?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3374eaf3f06eeb1ac4272d402cfa1b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac1e85463a3177f487d896b3d1d24c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
(3)定义函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0914c295f572c98dd043d4f84268934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9599b8c0f6a10d15f408ad651b35c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72878dfe2c7a76d76287194ac4bdf4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729b4033af5b0c9c4889406d2c8294f7.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a386e4d3f92631ed64ca3e2f5f4725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
2023-12-25更新
|
714次组卷
|
4卷引用:上海市静安区回民中学2024届高三上学期12月阶段性测试数学试题
上海市静安区回民中学2024届高三上学期12月阶段性测试数学试题(已下线)第五章 导数及其应用(单元重点综合测试)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)上海市浦东复旦附中分校2023-2024学年高三下学期3月月考数学试题湖南省邵阳市第二中学2024届高三下学期入学测试数学试题
名校
解题方法
5 . 若函数
满足:对任意的实数
,
,有
恒成立,则称函数
为 “
增函数” .
(1)求证:函数
不是“
增函数”;
(2)若函数
是“
增函数”,求实数
的取值范围;
(3)设
,若曲线
在
处的切线方程为
,求
的值,并证明函数
是“
增函数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9cec0474c43086ea39cb457048313c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dca031c9a6a1199cfee4c3d91c52099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916ae6490922319a1d394fbedd8d951a.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916ae6490922319a1d394fbedd8d951a.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b34671abe25726a52a57850ab248fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916ae6490922319a1d394fbedd8d951a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974f122681f314e8202e02861cabf8cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916ae6490922319a1d394fbedd8d951a.png)
您最近一年使用:0次
2023-12-21更新
|
723次组卷
|
4卷引用:上海市奉贤区2024届高三一模数学试题
上海市奉贤区2024届高三一模数学试题(已下线)上海市奉贤区2024届高三一模数学试题变式题16-21重庆市育才中学校2023-2024学年高二下学期三月拔尖强基联盟联合考试巩固测试数学试题四川省屏山县中学校2023-2024学年高二下学期第一次阶段性考试数学试题
名校
6 . 已知
.
(1)求函数
的单调区间和极值;
(2)请严格证明曲线
有唯一交点;
(3)对于常数
,若直线
和曲线
共有三个不同交点
,其中
,求证:
成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647014ad8af603468f4100043c4bde15.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720777756eaef6fd797e16c7656bd916.png)
(2)请严格证明曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720777756eaef6fd797e16c7656bd916.png)
(3)对于常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3387f1c69de6c2407212536b35150e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46111e4d12c21798aa213c0d7804c2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720777756eaef6fd797e16c7656bd916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3059524807d8e93433b8d994df6ede70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7169ce3255d2a02a20aa5932d2bd48.png)
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2023-12-19更新
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623次组卷
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3卷引用:上海市嘉定区2024届高三一模数学试题
7 . 已知函数
.
(1)求函数
的最小值;
(2)求函数
过点
的切线;
(3)就实数
的不同取值,讨论关于
的方程
的解的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851b3f76133c76d8942580296d3cf795.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa662f0273f0921c1fa4727f632395.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf03e87dd5d82d30fd01be26cee1f27.png)
(3)就实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d10c57dbf79c4ac05cc8592aed35585.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
,
,其中
为自然对数的底数,设函数
,
(1)若
,求函数
的单调区间,并写出函数
有三个零点时实数
的取值范围;
(2)当
时,
分别为函数
的极大值点和极小值点,且不等式
对任意
恒成立,求实数
的取值范围.
(3)对于函数
,若实数
满足
,其中F、D为非零实数,则
称为函数
的“
笃志点”.
①已知函数
,且函数
有且只有3个“
笃志点”,求实数a的取值范围;
②定义在R上的函数
满足:存在唯一实数m,对任意的实数x,使得
恒成立或
恒成立.对于有序实数对
,讨论函数
“
笃志点”个数的奇偶性,并说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2399c2a712a2890dcd0b195d3b9f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9deadf1801ba8ad09bc94db9279dbb5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21872d5d768a8041ab7bb57aa212ba0d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6551c3292a48d8d875298f54ef996cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff60eab72de85437e12806474281612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8454b9cade5319822d45cf53a90c8a31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882b660047bb6ded500cedba57958e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018a66c847609b6598fd455445021ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb270730495d3aa42e23c8b0d98ab3ae.png)
①已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51c0652d6fd46dab3783e17b9054993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587f9f6a4bfc5bdc31b32b03353a0cc3.png)
②定义在R上的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6945674f1cb97c868dde84129106e55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/674429107bdd48aa75e85a30d36e7276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc671b445f41402078b15e2ba6fdf8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb270730495d3aa42e23c8b0d98ab3ae.png)
您最近一年使用:0次
解题方法
9 . 已知
,定义极值点数列:将该函数的极值点从小到大排列得到的数列,对于任意的正整数n,判断以下两个命题:( )
甲:此数列中每一项都在
中.
乙:令极值点数列为
,则
为递减数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ee920bf197c6ed532e9ec42afc9697.png)
甲:此数列中每一项都在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3ca684ea4fc6a042241383d5ef4730e.png)
乙:令极值点数列为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4fa8ab268ba8f0da13d71e8817f136.png)
A.甲正确,乙正确 | B.甲正确,乙错误 |
C.甲错误,乙正确 | D.甲错误,乙错误 |
您最近一年使用:0次
2023-12-16更新
|
250次组卷
|
2卷引用:上海市嘉定区2024届高三上学期质量调研数学试题
名校
10 . 对于函数
,把
称为函数
的一阶导,令
,则将
称为函数
的二阶导,以此类推
得到n阶导.为了方便书写,我们将n阶导用
表示.
(1)已知函数
,写出其二阶导函数并讨论其二阶导函数单调性.
(2)现定义一个新的数列:在
取
作为数列的首项,并将
作为数列的第
项.我们称该数列为
的“n阶导数列”
①若函数
(
),数列
是
的“n阶导数列”,取Tn为
的前n项积,求数列
的通项公式.
②在我们高中阶段学过的初等函数中,是否有函数使得该函数的“n阶导数列”为严格减数列且为无穷数列,请写出它并证明此结论.(写出一个即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc50cb09e19e0d2d6aac80e1595c40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51350a90203fcdc2d500a89061b7f52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b211497c206bf64cbccfbc78b88cf284.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85b386e931b512e94ade91181aa8cc2.png)
(2)现定义一个新的数列:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d3a735f9848d5d727482a7f56d3ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee64825b2e41c93f1c368eab203a270b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
①若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4888beb7e1e150e0a9ad6b565dc18316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e468312d09c6563c9094b710a35a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3400dd0b134de441b93009d5b2549e.png)
②在我们高中阶段学过的初等函数中,是否有函数使得该函数的“n阶导数列”为严格减数列且为无穷数列,请写出它并证明此结论.(写出一个即可)
您最近一年使用:0次
2023-12-16更新
|
805次组卷
|
6卷引用:上海市嘉定区2024届高三上学期质量调研数学试题
上海市嘉定区2024届高三上学期质量调研数学试题上海市普陀区长征中学2024届高三上学期10月月考数学试题广东番禺中学2023-2024学年高三第六次段考数学试题(已下线)信息必刷卷05(上海专用)(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)广东省广州市番禺中学2024届高三第六次段考数学试题