名校
1 . 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
|
815次组卷
|
7卷引用:上海市高二下学期期末真题必刷04(压轴题)--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04(压轴题)--高二期末考点大串讲(沪教版2020选修)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(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)广东番禺中学2023-2024学年高三第六次段考数学试题广东省广州市番禺中学2024届高三第六次段考数学试题(已下线)信息必刷卷05(上海专用)
名校
2 . 已知
,设函数
的表达式为
(其中
)
(1)设
,
,当
时,求x的取值范围;
(2)设
,
,集合
,记
,若
在D上为严格增函数且对D上的任意两个变量s,t,均有
成立,求c的取值范围;
(3)当
,
,
时,记
,其中n为正整数.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68155558673dee3c3b339a73d752097.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e1d58efba7354ff2ccb96922732094.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0248255c35db564b386e4a997f822a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3e852eebd74ce9620a6baaef6d35fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d9a4cae3158b96893800ddc6ebbc76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/610a635570c8e84423dbf0f6a566c138.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a915c1a8a9304aeb307d130faaeb15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22f37cf574ebef90d4e1204db94bcbaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7203bef757822b5d482430f8bf80dea7.png)
您最近一年使用:0次
2023-04-13更新
|
1519次组卷
|
5卷引用:天津市南开中学2022-2023学年高二下学期期末数学试题
天津市南开中学2022-2023学年高二下学期期末数学试题上海市普陀区2023届高三二模数学试题天津市耀华中学2023届高三二模数学试题(已下线)重难点04导数的应用六种解法(1)(已下线)专题04 函数导数综合应用(四大题型)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(天津专用)
名校
3 . 已知
是函数
的极值点.
(1)求
;
(2)证明:
有两个零点,且其中一个零点
;
(3)证明:
的所有零点都大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea764080dd9860df23c7022ca914ea6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31ec7374ee26d32346f96ac1e03d2fd.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f13c1f9a7777c49671e1d6b4bb1e7f7e.png)
您最近一年使用:0次
2022-12-27更新
|
1432次组卷
|
4卷引用:江苏省扬州中学2022-2023学年高二上学期期末模拟数学试题
江苏省扬州中学2022-2023学年高二上学期期末模拟数学试题内蒙古呼和浩特第二中学2022-2023学年高三上学期12月月考数学文科试题河南省中原名校联盟2023届高三上学期12月教学质量检测数学文科试题(已下线)专题9 函数与导数 第5讲 导数与函数的零点问题
4 . 已知函数
(
),
(
).
(1)讨论函数
的单调性;
(2)当
时,函数
、
满足下面两个条件:①方程
有唯一实数解
;②直线
(
)与两条曲线
和
有四个不同的交点,从左到右依次为
,
,
,
.问是否存在1,2,3,4的一个排列
,
,
,
,使得
?如果存在,请给出证明;如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c73cf0d3363268899ede79d3058c1c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c98bf9d630346ad3447fe360c2534b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155c7f573e898da225390202da1767e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca29068fbc5a172fdc0e57eb04452ae.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/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2da6552c73bd45402979cd209dc530a0.png)
您最近一年使用:0次
2022-07-15更新
|
582次组卷
|
4卷引用:山东省菏泽市2021-2022学年高二下学期期末数学试题
山东省菏泽市2021-2022学年高二下学期期末数学试题山西省阳高县第一中学校2022-2023学年高二下学期期末数学试题(已下线)专题10 导数及其应用难点突破2-利用导数解决零点、交点问题-2(已下线)模块三 专题1 劣构题专练【高二下人教B版】
名校
5 . 若函数
的定义域为
,对任意的
,
恒成立,则称函数
为“有下界函数”,其中
的最大值称为函数
的“下确界”.已知函数
,其中
.
(1)若
,证明:
为“有下界函数”,并求出
的“下确界”.
(2)若函数
为“有下界函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796629d1136615f7891f0e5cd7f926ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d4409c3166f7229ca07183d3952085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](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/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
6 . 已知
,函数
.
(1)若
的极小值为0,求a的值.
(2)当
时,函数
,证明:
无零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe57c09ce4f23c0ef11ad30da31d4c20.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c800d9316e29111c83ce1af04f3544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
名校
7 . 对于定义在D上的函数
,其导函数为
.若存在
,使得
,且
是函数
的极值点,则称函数
为“极致k函数”.
(1)设函数
,其中
,
.
①若
是单调函数,求实数a的取值范围;
②证明:函数
不是“极致0函数”.
(2)对任意
,证明:函数
是“极致0函数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7807143d8a2929459b46063519843f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0da9fd5dfe735b958eb002702baa2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48196cf98394fcbce4181c33754141dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375a66a688f4a9133fde13d212901c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bffdee54569b89c743b86a90f28b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc26fdf6289ac213b712cc32619e1e2.png)
您最近一年使用:0次
2021-11-04更新
|
973次组卷
|
5卷引用:上海市建平中学2021-2022学年高二下学期期末数学试题
上海市建平中学2021-2022学年高二下学期期末数学试题辽宁省部分学校2024届高三上学期期末数学试题(已下线)上海市高二下学期期末真题必刷04(压轴题)--高二期末考点大串讲(沪教版2020选修)北师大版(2019) 选修第二册 突围者 第二章 第六节 课时2 函数的极值(已下线)重难点04导数的应用六种解法(2)
8 . 已知
为自然对数的底数,
.
(1)求
的单调区间;
(2)证明
有且仅有两个零点;
(3)问:函数
与
的图象有几条公切线?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6bf7c3198cdd4dafc81e3992f34bd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f184f195e983df4014e6c57a2e7ee67.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575df2758d348d7d5b889fb5ad8ddafe.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575df2758d348d7d5b889fb5ad8ddafe.png)
(3)问:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
您最近一年使用:0次