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1 . 已知函数
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45f1d8728779d4e4b0534a5c1721602.png)
A.函数![]() ![]() ![]() |
B.函数![]() |
C.函数![]() ![]() |
D.函数![]() |
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2卷引用:广东省佛山市南海区第一中学2023-2024学年高二下学期阶段三暨期末统考模拟检测数学试题
2 . 已知
.
(1)求
的极值;
(2)画出函数
的大致图象;(注意:需要说明函数图象的变化趋势)
(3)若函数
至多有一个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0c7ebf02ecb75a6f98d39085a8dbb8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3d930126d2025a5242a192cf414b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 已知函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6463b3ff9900061f267f612d3d2b7633.png)
A.函数![]() |
B.若方程![]() ![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() ![]() |
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4 . 已知某绿豆新品种发芽的适宜温度在
之间,一农学实验室研究人员为研究温度
与绿豆新品种发芽数(颗)之间的关系,每组选取了成熟种子50颗,分别在对应的
的温度环境下进行实验得到如下散点图:
与
的关系,请计算相关系数 加以说明,并建立
关于
的回归方程;
(2)研究发现
关于
的回归方程刚好与函数
在点
处的切线重合,求
,
的值并求函数
的单调区间以及极值.
参考数据:
,
,
,
.
参考公式:相关系数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b729c908e5cbd2448117f474641ebc9a.png)
最小二乘估计公式分别为
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a263e872bfd1d9b934ced5b38185b0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d344d2cb644e80406045f8a2cb060fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b1182ede007b9d7adccea5837dcb232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)研究发现
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0d13bfc768d52b1a96032d73c041f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fed487c0befbc23bc5a885bcdd6c755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be865ca9c4ac7374ae41e8b54de30fbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f1b4e3969acadf48bc79010200d99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da75e56c78f6d05f01ccaa09a4bd9a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94622f25312f8878643d355da5075f6d.png)
参考公式:相关系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b729c908e5cbd2448117f474641ebc9a.png)
最小二乘估计公式分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da681f395dbaeeb19432f63b6f1a39ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390fb5e906a242d833cc0068ff23efc2.png)
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5 . 已知函数
.
(1)若
是函数
的极值点,求
的值,并求其单调区间与极值;
(2)若函数
在
上仅有2个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b330b5d585ec1bb51fb1d68b49150bf8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2024-05-08更新
|
444次组卷
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6 . 已知函数
,过点
可作
条与曲线
相切的直线,则实数
的取值范围是______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdfe48038034eb671b3852e261c24f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5199549b47e180b07cb219ae40c9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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7 . 已知函数
,定义
表示不超过
的最大整数(如
).
(1)若
在
上单调递增,求实数
的取值范围;
(2)已知当
时,
有唯一极大值
,此时令![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
. 对
,若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53219f63721ef5731f5b1e07ffc6303d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d54a0e82778f606d95a486835ac9f56.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521976f4b831d5e16926de504af83567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f429e3b5f3e5fa07ac120ce42aacdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4761151a69551a7fed269fa9fe992a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c3b2f14e4591a5c15ef0ee73aade7bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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8 . 已知函数
,
(1)求
的极小值;
(2)讨论方程
的实数解的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf641f6e0b4993b47c9db06b2a8e0910.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)讨论方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1602d26f37ad945a5e159a1e43cfdb7.png)
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9 . 已知函数
为实数,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4889dcf212fdd165b1da68bfe18e99.png)
A.当![]() ![]() ![]() |
B.存在![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.若函数![]() ![]() ![]() ![]() |
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10 . 给定函数. ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2344cb96f30d1f03c4913caab13dc4d.png)
(1)求
的极值;
(2)讨论
解的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2344cb96f30d1f03c4913caab13dc4d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91458308a7515821a07a3a63e325e474.png)
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2024-04-18更新
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