2023高二·上海·专题练习
解题方法
1 . 已知函数
,其导函数
的图象经过点
,
,如图所示,则下列说法中正确结论的序号为_____ .
时函数取得极小值;
②
有两个极值点;
③当
时函数取得极小值;
④当
时函数取得极大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb885b96ddbf9889de11e3339ca7704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d599059e6b2c918ab15ee22611b6962.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
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2 . 在下列命题中,正确命题的序号为______ (写出所有正确命题的序号).
①函数
的最小值为
;
②已知定义在
上周期为4的函数
满足
,则
一定为偶函数;
③定义在
上的函数
既是奇函数又是以2为周期的周期函数,则
;
④已知函数
,若
,则
.
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf93d556716be1d6082a0355a07bfb16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8aae28ca96120a3ec1f4ce541db3580.png)
②已知定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aeeb9b81e3c6a0d36add7093b657832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
③定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9626c180cc029e80e9b3b008038c67d.png)
④已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37aa94fb49142178126bf4d6730af798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ecda7bfb0a2043306bf7707a136ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74fe8b70a97156754d8e878f6607719.png)
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2021-07-22更新
|
200次组卷
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2卷引用:黑龙江省哈尔滨市第九中学2020-2021学年高二下学期期末考试文科数学试题
3 . 已知函数
和
,若
,现有下列4个说法:①
;②
;③
;④
.其中所有正确说法的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9cc7f5b6853e3e6d0b8ba16ea81edc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9963dcc20d9a6467213797e65f947426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23b2604e5f8be78fbe6cafcb9b7f2f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/419504736c4934f6e0df4114c3743944.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a42526840a0fc525571737bed3d1af6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e431fbe9d32c1fb868e4e3d2e1bd81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d9b616bddad1c2d129975b2a3067603.png)
A.①②④ | B.①②③ | C.②③ | D.①③④ |
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2022-07-07更新
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2卷引用:河南省南阳市2021-2022学年高二下学期期末数学理科试题
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解题方法
4 . 已知函数
给出下列结论:
①
在
上有最小值,无最大值;
②设
则
为偶函数;
③
在
上有两个零点.
其中正确结论的序号为________ .(写出所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7e727929a1fe64d3da9f9dc4b64b9e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c2e00e0ba21405c6c8221f2248a08cd.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a019d93dff2f07e177247365550659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754d3d2a36a239b8b98db7838d9e0ee.png)
其中正确结论的序号为
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11卷引用:黑龙江省七台河市勃利县高级中学2020-2021学年高二4月月考数学(文)试题
黑龙江省七台河市勃利县高级中学2020-2021学年高二4月月考数学(文)试题(已下线)模块3 专题3 第2套 小题入门夯实练【高二人教B】2020届北京市平谷区高三第二次模拟考试数学试题北京市平谷区2020届高三第二学期阶段性测试(二模)数学试题考点05 导数的应用-2020年【衔接教材·暑假作业】新高三一轮复习数学(理)(人教版)考点05 导数的应用-2020年【衔接教材·暑假作业】新高三一轮复习数学(文)(人教版)(已下线)第二单元 函数概念与基本初等函数(B卷 滚动提升检测)-2021年高考数学(文)一轮复习单元滚动双测卷(已下线)专题13 函数及其性质-2020年高考数学母题题源解密(北京专版)(已下线)考点45 导数与函数的极值、最值-备战2021年新高考数学一轮复习考点一遍过北京市首都师范大学第二附属中学2021届高三下学期开学考试数学试题(已下线)北京市海淀区2022届高三一模数学试题变式题11-15
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5 . 设函数
下列命题:
①
的解集是
,
的解集是
或
;
②
是极小值,
是极大值;
③
没有最小值,也没有最大值;
④
有最大值,没有最小值.
其中正确的命题序号为__________ .(写出所有正确命题的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/791956b918f2b45654ff4422a3f50d80.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b9d7630a0ac7cd9af9a87876da9db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae6c32f0fafbbd03833f64b3ef60caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/890d6dafa253b76e17c37f607ad29a53.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fe45ecd5d507adc2e7ffc1b1755856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb71ad742b421a7ba62d8c1923d33358.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
其中正确的命题序号为
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2卷引用:北京市西城156中2016-2017学年高二下学期期中考试数学(文)试题
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6 . 已知
,函数
有两个极值点
,则下列说法正确的序号为_________ .
①若
,则函数
在
处的切线方程为
;②m可能是负数;
③
;④若存在
,使得
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f1d37d41130c72ae150a64ddb2f949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b21672fd907c5c92fee1d649e7003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf46dc84732526c826d84a71c407ea89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f7fbfa2214ca72495a993b2fed8b61.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f8f79e938bf77f67440579ad10cb82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07ad90ca228230b03f12eb48ee0c1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eaa6773bd23f36a1577f8456ae6ae86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c9c27cc04aca332fb3098228a1119b3.png)
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2卷引用:天津市重点校2023-2024学年高二下学期4月期中联考数学试题
7 . 设
是函数
的导函数,若对于任意的实数x,都有
,给出下列命题:①
是定义域上的增函数;②
;③
的最小值为
;④函数
恰有1个零点.其中正确命题的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceec72ad249f0ef8750d12a473148688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2c1b94d085032398ba2a3473c52edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d2356758a542b0808ef040354354228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec887a5238c1ec5e48fad4076282b75.png)
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8 . 对于函数
,给出下列四个结论:
①
是奇函数;
②方程
有且仅有1个实数根;
③
在
上是增函数;
④如果对任意
,都有
,那么
的最大值为2.
其中正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707dd66e0d6f8c33c6e05b4555f12c31.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/becd598a11b876d858728161a7a09705.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
④如果对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8800c695cb799480fe1eb3859868e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
其中正确结论的序号为
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9 . 给出下列命题:
①
②
③
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8243132b881c61584062214e85a3b00.png)
其中正确命题的序号为__________ .
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa31ba8de8f2e0f6b079b73d57ddc4a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5d87a925c5d67e00f7e9834a6a78e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf27641feeea025d7ead6e146a590619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8243132b881c61584062214e85a3b00.png)
其中正确命题的序号为
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10 . 丹麦数学家琴生是
世纪对数学分析做出卓越贡献的巨人,特别是在函数的凹凸性与不等式方面留下了很多宝贵的成果.定义:函数
在
上的导函数为
,
在
上的导函数为
,若在
上
恒成立,则称函数
是
上的“严格凸函数”,称区间
为函数
的“严格凸区间”.则下列正确命题的序号为 ____________ .
①函数
在
上为“严格凸函数”;
②函数
的“严格凸区间”为
;
③函数
在
为“严格凸函数”,则
的取值范围为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be7581dbbccda50e5d5cd18056ddea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06797f73d23dd870776d8b113cc73920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06797f73d23dd870776d8b113cc73920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06797f73d23dd870776d8b113cc73920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa4b560c48799ad63736f4fbca9b0ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06797f73d23dd870776d8b113cc73920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06797f73d23dd870776d8b113cc73920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c482e2e4631a33f5a1206901c8e9a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a9a5cc93a7d225c28c4c794dcbaa53.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f53f81bca037a4383c1fab122a3cd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcb304ae8313cab66b0eba70e43b0688.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1807569c10a19abeab5c5587684049d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74b9c316274c21fe4812bdd66eb40d0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85708d2da706ab970ceab57336c23f15.png)
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