名校
1 . 已知函数
是定义域为
的可导函数,若
,且
,则( )
![](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/ee0b94eef7875086f8aff56d4e1de81e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1d88f08209350ff227f0f4ddba626b.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
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解题方法
2 . 柯西中值定理是数学的基本定理之一,在高等数学中有着广泛的应用.定理内容为:设函数
,
满足①图象在
上是一条连续不断的曲线;②在
内可导;③对
,
.则
,使得
.特别的,取
,则有:
,使得
,此情形称之为拉格朗日中值定理.
(1)设函数
满足
,其导函数
在
上单调递增,判断函数
在
的单调性并证明;
(2)若
且
,不等式
恒成立,求实数
的取值范围;
(3)若
,求证:
.
![](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/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9b92a1988f20c45e8ba3887eeb6b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce5b83b652a50ea15c83c826d8fb52f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38593523a246f9e59688f64444e0dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a1212aca40e8dfbb97ae428c5d40a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4306fb6d5419322b4b7b9140e06e43a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38593523a246f9e59688f64444e0dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584ef8a5b63c5a2a80372865ac0cc0a0.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acaa791feb147bd1a8bf5eb4f81a0cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a4b4a9b7f0a8c3de045fe903204800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e71b49ac6c97943138bed91aab6215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d64f25e0020c3db48bb6a767afa98a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19cf16fd398ad9782cd4f5149d0c76f.png)
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3 . 已知函数
有三个零点
,
,
,其中
,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3c506fac3a1f05033077859e21ea6b.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/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31dac77855629d41746583d4ed44592.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知函数
,若关于
的方程
恰有四个不同的实数根,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d499422674838aa176019fb7ca1eb19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd5ffba5a195bb8a0a37d2060b4b994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-04-26更新
|
665次组卷
|
10卷引用:重庆市重庆市长寿区重庆市长寿川维中学校2023-2024学年高二下学期5月月考数学试题
重庆市重庆市长寿区重庆市长寿川维中学校2023-2024学年高二下学期5月月考数学试题江西省赣州市六校联考2021-2022学年高二下学期期中数学(理)试题福建省华安县第一中学2022-2023学年高二下学期期中考试数学试题福建省莆田第十五中学2022-2023学年高二下学期期中测试数学试题福建省宁德市霞浦县宏翔高级中学2022-2023学年高二下学期第一次段考数学试题广东省东莞市三校2023-2024学年高二下学期4月期中联考数学试题广东省东莞市光明中学2023-2024学年高二下学期期中考试数学试卷(已下线)5.3.2函数的极值与最大(小)值(3)江西省八所重点中学2022届高三4月联考数学(文)试题(已下线)模块2专题8零点问题 方程图象练
解题方法
5 . 若不等式
对任意的
恒成立,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b183b53013253e4410e7597087222a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c173a7bdba9681b71d7348e53b9af6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-04-20更新
|
2084次组卷
|
5卷引用:重庆市部分学校2023-2024学年高二下学期4月阶段性测试数学试卷
名校
解题方法
6 . 函数
是定义在
上的奇函数,其导函数为
,且
,当
时,
,则关于
的不等式
的解集为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9a3bc1b2142871d56b78c2cc57ce73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5aebe20397ea9441d0fcebfda55922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60766b0c3705ffe3e62fe42931022617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b32c8047ddaf882b04af49019f69e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-04-17更新
|
698次组卷
|
6卷引用:重庆市礼嘉中学2023-2024学年高二下学期第一次月考数学试题
重庆市礼嘉中学2023-2024学年高二下学期第一次月考数学试题(已下线)模块一 专题4 【讲】《导数的概念、运算及其几何意义》(人教B2019版)安徽省六安市裕安区新安中学2023-2024学年高二下学期第一次月考数学试题(已下线)模块一 专题5《导数的概念、运算及其几何意义》【讲】(高二北师大版)(已下线)第二章导数及其应用章末十八种常考题型归类(4)云南省下关第一中学2023-2024学年高二下学期5月期中数学试题
7 . 若实数
,
分别是方程
,
的根,则
的值为______ .
![](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/22c8cd775fba88d87428dab41260b308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b953e06f7a01faeace7176ddd2d77c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3049273653a7a4d7f6252d0c1f05164.png)
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|
465次组卷
|
2卷引用:重庆市拔尖强基联盟2023-2024学年高二下学期三月联合考试数学试题
名校
8 . 已知函数
的定义域为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc91d7e6942fca54524ec1c945c31a52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5553f71f343e2fcbafbaaf42ef8ce8b7.png)
A.![]() ![]() ![]() | B.![]() ![]() |
C.![]() | D.![]() |
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9 . 已知函数
.
(1)求函数
在
处的切线方程;
(2)讨论函数
在区间
上的单调性;
(3)证明函数
在区间
上有且仅有两个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720c16ff497902c3eaa35fff95c8438a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(3)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/710025944c47bfd0b2402b2e49e41d04.png)
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解题方法
10 . 设函数
在区间
上可导,
为函数
的导函数.若
是
上的减函数,则称
为
上的“上凸函数”;反之,若
为
上的“上凸函数”,则
是
上的减函数.
(1)判断函数
在
上是否为“上凸函数”,并说明理由;
(2)若函数
是其定义域上的“上凸函数”,求
的取值范围;
(3)已知函数
是定义在
上的“上凸函数”,
为曲线
上的任意一点,求证:除点
外,曲线
上的每一个点都在点
处切线的下方.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882d17c122eb8008105e85d55bf55587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e152e9080da9afb2e1356459d2c9b656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6221357dde18e25a5c1b92a289b3a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48e20aab9970576ac56a59fed9c3f8b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48e20aab9970576ac56a59fed9c3f8b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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