名校
1 . 设函数
的导函数为
的导函数为
的导函数为
.若
,且
,则
为曲线
的拐点.
(1)判断曲线
是否有拐点,并说明理由;
(2)已知函数
,若
为曲线
的一个拐点,求
的单调区间与极值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a00a7220fe1f1699aa32ea0c70a303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2183b5237f02670ccbe463aaaca37977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0b72923071c1010a36f17cb3d1168b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca411f2905fd482bd14cb0092e5a6279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9154699908e7a530d9e04830c9315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c683786f6c924632d9ca47ea243700e7.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/341534f0072c55c40cc00ed25097c2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9bfaad7a770a2bb3930de1ed7444d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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5卷引用:辽宁省沈阳市第二中学2024届高三下学期三模数学试题
(已下线)辽宁省沈阳市第二中学2024届高三下学期三模数学试题河南省部分重点高中2023-2024学年高三下学期5月联考数学试卷 (新高考)2024届青海省海南藏族自治州高考二模数学(理科)试卷内蒙古自治区锡林郭勒盟2024届高三下学期5月模拟考试理科数学试题(已下线)拔高点突破05 函数与导数背景下的新定义压轴解答题(九大题型)
名校
解题方法
2 . 已知函数
及其导函数
的定义域均为
,若
是奇函数,满足
,且对任意
,
,
,则( )
![](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/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01a4717b971daeae2bf1f9370c9ce8c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f370a1d4dd341e5ab1774a66c66c1204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89867b421750df2435356f115bfd8c29.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 已知a,
,若
,
,则b的可能值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07de49f290b3fd36733d129379d19c8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efdc0e0ca559f0f1af6127545f356fa2.png)
A.2.5 | B.3.5 | C.4.5 | D.6 |
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2卷引用:2024年辽宁省普通高等学校招生全国统一考试(模拟2)数学试题
4 . 在
中,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41de4d71f031a145ffee28a1c487baed.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854e68b995b672792bb915ef502fcd5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41de4d71f031a145ffee28a1c487baed.png)
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名校
5 . 已知函数
.
(1)当
时,求曲线
在
处的切线方程;
(2)当
时,证明:
为单调递增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6687279e5f0000eb9d36582b8e1a1e63.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe45993e6bd636a4f34886bb3d72f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2卷引用:2024年辽宁省普通高等学校招生全国统一考试(模拟2)数学试题
解题方法
6 . 设A,B是两个随机事件,且
,
,则下列正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2dc39b48969812063cc9d265489e10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f265833907c74d5d9771f0383c6b76.png)
A.若![]() | B.![]() |
C.![]() | D.A与B有可能是对立事件 |
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名校
解题方法
7 . 已知函数
,将
的图象向右平移
个单位长度,得到函数
的图象,则函数
的值域为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d7f6e1cbe0d9005b2fad3345a8b017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd9bb0a0ce6bb97c05dbf5b2aa64f98.png)
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8 . 如图,已知菱形ABCD和菱形ADEF的边长均为2,
,
,M,N分别为AE、BD上的动点,且
.
平面EDC;
(2)当MN的长度最小时,求AF与平面MND所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31285c747ac70d3ea0beac9b658d027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793e03b60fc5ac445d6d44c508e7e73e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b138770c405307ea4fc828624645e2c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
(2)当MN的长度最小时,求AF与平面MND所成角的正弦值.
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名校
9 . 已知
,那么
的近似值为______ .(保留小数点后一位数字)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2493a9847bdf4e7e0cb5da764d62a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cf6d10885fb83ded00d4e39532fcd10.png)
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名校
解题方法
10 . 如图,在长方体
中,
,
,
是棱
上的一点,点
在棱
上,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/1/a32ef7ea-03be-4bb9-9d57-ca872cb326a9.png?resizew=145)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/1/a32ef7ea-03be-4bb9-9d57-ca872cb326a9.png?resizew=145)
A.若![]() ![]() |
B.存在点![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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2卷引用:辽宁省沈阳第二中学2024届高三第四次模拟考试数学试卷