1 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efbf2dc90f32ba8d10297600582a6f3e.png)
(1)当
时,求
在
上的值域;
(2)若方程
有三个不同的解,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efbf2dc90f32ba8d10297600582a6f3e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9c64ba837387d640de4b8e2191b1b5.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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解题方法
2 . 设实数
,若对任意的
,不等式
恒成立,则
的最大值是______ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1abded90495e9d6ed95277ae2dee3bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a9774872925b4f9a87f401fd782dfb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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3 . 已知函数
的导函数
的图像如图所示,下列说法不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
A.函数![]() ![]() | B.函数![]() ![]() |
C.函数![]() ![]() | D.函数![]() |
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2卷引用:贵州省黔西南州金成实验学校2023-2024学年高二下学期4月月考数学试题
名校
4 . 函数
的导函数为
的图象如图所示,关于函数
,下列说法不正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/27/f0f7b152-eb3b-450c-896e-395292c137c0.png?resizew=152)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/27/f0f7b152-eb3b-450c-896e-395292c137c0.png?resizew=152)
A.函数![]() ![]() |
B.函数在![]() ![]() |
C.函数存在两个极值点 |
D.函数有最小值,但是无最大值 |
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7卷引用:贵州省遵义市2021-2022学年高二下学期期末质量监测数学(文)试题
贵州省遵义市2021-2022学年高二下学期期末质量监测数学(文)试题上海市曹杨第二中学2022-2023学年高二下学期期中数学试题上海市曹杨中学2022-2023学年高二下学期期中数学试题(已下线)期末模拟预测卷02(测试范围:平面解析几何,计数原理与概率统计,函数与导数,空间向量与立体几何)(原卷版)(已下线)上海市曹杨第二中学2023-2024学年高二下学期期中考试数学试卷(已下线)专题05导数及其应用全章复习攻略--高二期末考点大串讲(沪教版2020选修)(已下线)核心考点2 导数几何意义和函数的单调性、极值 专题讲解 A基础卷 (高二期末考试必考的10大核心考点)
解题方法
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3bd9536fa068918321bc80abad38f7c.png)
(1)当
时,求函数
的最小值;
(2)
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3bd9536fa068918321bc80abad38f7c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e81b4aac721bcd4a49593b48a28a8f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7日内更新
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430次组卷
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2卷引用:贵州省六盘水市2023-2024学年高二下学期5月期中质量监测数学试题
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6 . 已知定义在
上的函数
满足:
,则不等式
的解集为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea729e249a43cf07c31634ab3b4c98d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7623bb7c826abc714235ef0e7052ad08.png)
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7 . 帕德近似(Pade approximation)是法国数学家帕德(Pade)于l9世纪末提出的,其基本思想是将一个给定的函数表示成两个多项式之比的形式,具体是:给定两个正整数m,n,函数
在
处的
帕德近似为
,其中
,
,
,…,
(
为
的导数).已知函数
在
处的
阶帕德近似为
.
(1)求实数a,b的值;
(2)证明:当
时,
;并比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b73a1e9e6afa355710753d576ea991a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8cd76f42911e8c8e57ce761b4541137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52140f46c02b2bde412f89d0977bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85cd03aea30c3ee0093afad048b75c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b63504a4bf0d4861de7909bbc2e4878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd370c3b127fbdb77b6e5c40318328d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2db1e56c92e2ebdc5d2cae336a01b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e96546b3259afe4add331673fb835c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d307aa65d930bc8e51835eb147de513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96d128f7851b7771f95bffbdbf3ced02.png)
(1)求实数a,b的值;
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d0af421900f7a55f52dd805064f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4548db97a06a6f27db6af1dd9b063645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786a32019158f0d2ec126cf189ccf572.png)
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8 . 正弦型函数被广泛运用于信号处理领域.将不同周期的正弦型函数叠加,就可以构建各种各样的信号.如
就能构建一种信号,关于该函数,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f049267c4eff2f6028d6a83c04e43c.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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9 . 已知
是
上的偶函数且满足
,若对
,
恒成立,则实数a的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0780c37e42419d65bdabf31b41f24934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d70d2a3c9ff48faf18a6f2acd79d8f.png)
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10 . 设
是函数
的导函数,若
可导,则称函数
的导函数为
的二阶导函数,记为
.若
有变号零点
,则称点
为曲线
的“拐点”.
(1)研究发现,任意三次函数
,曲线
都有“拐点”,且该“拐点”也是函数
的图象的对称中心.已知函数
的图象的对称中心为
,求函数
的解析式,并讨论
的单调性;
(2)已知函数
.
(i)求曲线
的“拐点”;
(ii)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](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/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)研究发现,任意三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
![](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/211aed3f74a18399b2adbcb74420037e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e88ebfb5c0d6cce558b515be06404d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea257a36c48ae67291bb79295085a5d.png)
(i)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2342ead0be84f52b93d85f167fdbb9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1bb642f5f896ed02ecd76d9a15e500.png)
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