名校
1 . 已知函数
,给出以下说法:
①当
有三个零点时,
的取值范围为
;
②
是偶函数;
③设
的极大值为
,极小值为
,若
,则
;
④若过点
可以作
图象的三条切线,则
的取值范围为
.
其中所有正确说法的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e274d6bb0f7e618dcec88bb2791cdcf.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4208889a65489ead5fc22fae3ca26dd9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/649ae1af4ab147dd31a773141cdd47d1.png)
③设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee99ca13d8b9948a264d82838b1c436d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
④若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c47bcfe2d1bd9af0b9d80cb1ca9e0b.png)
其中所有正确说法的序号为
您最近一年使用:0次
名校
解题方法
2 . 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
您最近一年使用:0次
2020-09-09更新
|
570次组卷
|
11卷引用:2020届北京市平谷区高三第二次模拟考试数学试题
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)北京市海淀区2022届高三一模数学试题变式题11-15(已下线)模块3 专题3 第2套 小题入门夯实练【高二人教B】
名校
解题方法
3 . 若存在实常数
和
,使得函数
和
对其公共定义域上的任意实数
都满足
和
恒成立,则称直线
为
和
的“隔离直线”.已知函数
,
,
,则有下列命题:
①
与
有“隔离直线”;
②
和
之间存在“隔离直线”,且
的最小值为
;
③
和
之间存在“隔离直线”,且
的取值范围是
;
④
和
之间存在唯一的“隔离直线”
.
其中真命题的序号为_______________________ .(请填上所有正确命题的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e593828316139a54019e352dec883f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21a7730d9983b6e8738a091c505d558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca2907f541536d6a8776aba673bcad77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e593828316139a54019e352dec883f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff0c1800ae34c5a7c5efc3d9296dc57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c2c579202ee1e98f4525a2aaaca778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f9d182316aec2c6af0abdc49191ba2.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ca0e0b071265e90852d22ef88de865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
②
![](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/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
③
![](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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b39f15729c7b85f666ce498fcd6203.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17432e76b39908abe390d80f3c97f476.png)
其中真命题的序号为
您最近一年使用:0次
2021-01-16更新
|
740次组卷
|
4卷引用:黑龙江省哈尔滨市第九中学2020-2021学年高三上学期期末考试理科数学试题
名校
4 . 若存在实常数k和b,使得函数
对其公共定义域上的任意实数x都满足:
恒成立,则称此直线
的“隔离直线”,已知函数
(e为自然对数的底数),有下列命题:
①
内单调递增;
②
之间存在“隔离直线”,且b的最小值为
;
③
之间存在“隔离直线”,且k的取值范围是
;
④
之间存在唯一的“隔离直线”
.
其中真命题的序号为__________ .(请填写正确命题的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef655f5ecd8e5f7798c6e6747ba999b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c34f5d4207fbf261bdbcf0926155230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c17624c234559f04f5d94b7077f169a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55adeff09c4d3d878785239f0bf2e27a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc247e5237219a6169648a3d20483c9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b814095580525ddc8176650af6b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b814095580525ddc8176650af6b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c768cd9231a15caad0839f05d0f9207c.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8945c5bbc31c6617924d2c8aa29a091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17432e76b39908abe390d80f3c97f476.png)
其中真命题的序号为
您最近一年使用:0次
2018-09-02更新
|
1123次组卷
|
5卷引用:【全国市级联考】山东省日照市2018届高三校际联考理科数学试题
名校
5 . 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)
您最近一年使用:0次
6 . 已知函数
.给出下列四个结论:①函数
的图象存在对称中心;②函数
是
上的偶函数;③
;④若
,则函数
有两个零点.其中,所有正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a647e5a0da7ef185fcc3511c10d8467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66d61d5f66d68b4c4a2a25fd7103621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9965004da00237069594dfc0c794df13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0767a92fe059b6ee0e7882f96aa12571.png)
您最近一年使用:0次
2023-07-22更新
|
136次组卷
|
2卷引用:四川省凉山州2022-2023学年高二下学期期末考试文科数学试题
7 . 如下关于函数
的说法:
①该函数始终有两个零点;
②当函数
取得最大值时对应的
满足关系:
;
③若该函数有两个零点
、
且
,当
取得最小值时,满足:
.
正确的序号为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab881028b86a66795256c9f44049dae.png)
①该函数始终有两个零点;
②当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba319a8ac97b1339b2f6f27f0909cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a302eda25ef93bbdb2d2b7e57083cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9087a2c0628517d2a23b34031623e58f.png)
③若该函数有两个零点
![](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/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93c54705d32dc6820f1a90eec2225dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d908fb12336e377c5a5ffc0cd2aa0e.png)
正确的序号为
您最近一年使用:0次
名校
解题方法
8 . 关于函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d42bc1614c3372edf362b4c07154fba.png)
(1)
是
的极小值点;
(2)函数
有且只有1个零点;
(3)
恒成立;
(4)设函数
,若存在区间
,使
在
上的值域是
,则
.
上述说法正确的序号为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d42bc1614c3372edf362b4c07154fba.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac5b738cd5ea12f6d93e9c5fc6bcd5.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afe29938b4ed7cb7d45448089a8a40a3.png)
(4)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652f22f72087b987613d5f25ef342070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa9672a543dff72e64cf71ff0d3096.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/d6a74d044a20150362a78457c3e52b79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f33f11c79698185b1239b5f8626853.png)
上述说法正确的序号为
您最近一年使用:0次
2020-05-04更新
|
352次组卷
|
2卷引用:河北省石家庄一中2019-2020学年高三下学期3月质检数学(理)试题
解题方法
9 . 已知实数
满足
,给出下列结论:
①
;②
;③
;④
.
则所有正确结论的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e004fa02750b5e4f48dbab8a3a9d8a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed37ee7432002cd0e0978b2012e184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9707dcd2a38e5cb5fe8222ccacb3e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25f2c46d9ee7d9ce21f91738cf7b133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578bfa2ed37d074ec6b37285c5339699.png)
则所有正确结论的序号为( )
A.①③ | B.②③ | C.①②④ | D.②③④ |
您最近一年使用:0次
10 . 关于函数
,给出下列四个结论:
①
是奇函数;
②0是
的极值点;
③
在
上有且仅有1个零点;
④
的值域是
.
其中,所有正确结论的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a06840005b96bdb51970954a70bd07.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②0是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e03afd5d2c4c35e1f0ad6d97636ea549.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
其中,所有正确结论的序号为
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