20-21高二·全国·单元测试
解题方法
1 . 已知二次函数
,关于
的不等式
的解集为
,其中
为非零常数,设
.
(1)求
的值;
(2)
如何取值时,函数
存在极值点,并求出极值点.
(3)若
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3289d2e4520c5b872e814959bc3bed4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08bbe508332272fd1769bb2b87de3805.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987ee644169ad93379283ae715d8ebf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbd77a292834deca9109cfeae8d00e9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6944a8bd2626880b18de6424a4400c60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e965748980da1f255beabd63032e56.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fff88dfd467a01b177854545de17534a.png)
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2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f81694c250c0107d608508c094f27f.png)
(1)当函数
有3个零点,求实数
的取值范围;
(2)当
取条件(1)下的取值时,设函数
有3个零点
,
,
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f81694c250c0107d608508c094f27f.png)
(1)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a42945a6ff4452dfbe550e0f28c82f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcefa1eadaa807e3fe6c61a2f8d2dea9.png)
![](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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5646305daf3f3a5c135d45dbe51aff69.png)
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3 . 已知函数
(a为常数).
(1)若函数
是增函数,求a的取值范围;
(2)设函数
的两个极值点分别为
,
(
),求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213611317e843998c672932588cafe21.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](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/13e21ac584efecd770c2dd9d2e83803a.png)
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4 . 已知
有两个不同的零点
.
(1)求实数a的取值范围;
(2)若
,且
恒成立,求实数
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38572ad4ef879663d599510d64c4020f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2aabc96b7433bba077ceac76d8f0d75.png)
(1)求实数a的取值范围;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a42bb64f8a7ba48cd41e3163c33e95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec2e06edc27a6930c32f3450b0fb928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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名校
5 . 已知关于
的函数
为
上的偶函数,且在区间
上的最大值为10.设
.
(1)求函数
的解析式.
(2)若不等式
在
上恒成立,求实数
的取值范围.
(3)是否存在实数
,使得关于
的方程
有四个不相等的实数根?如果存在,求出实数
的范围,如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b39a21c80ae3e990027ecea33bfb6424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85564659d145e38c0887d186db1c8573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba94b35258a2fbde34d7e26be524fb6e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e567c3e841ba226b51543b0dc43e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4d001c51cf7b47102f641ded56b01b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6544efd3f7cea29d879628d508f0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2020-12-26更新
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2312次组卷
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8卷引用:江苏省扬州市2017~2018学年度高一第一学期期末调研测试数学试题
名校
6 . 已知函数
.
(1)当
时,求
在
处的切线方程;
(2)令
,已知函数
有两个极值点
,且
,
①求实数
的取值范围;
②若存在
,使不等式
对任意
(取值范围内的值)恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732a081df910f7b85a9d29dd139e2e6c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/005f2e6bee90297bd1c2c6533d29a87a.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7006220d33024798081a6f2c1d94c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58c4411628935f2c4a42095c9a644ca.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d001e8728b32aa28b83a9a36e674f9e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1b8af65459ae7ef940ef1589ee4d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2020-03-17更新
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1111次组卷
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7卷引用:天津市东丽区第一百中学2019-2020学年高三上学期第二次月考数学试题
天津市东丽区第一百中学2019-2020学年高三上学期第二次月考数学试题天津市西青区2019-2020学年高三第一学期期末考试数学试题2020届江苏省南京师大附属扬子中学高三下学期期初数学试题(已下线)专题08 巧辨“任意性问题”与“存在性问题(第一篇)-2020高考数学压轴题命题区间探究与突破天津市蓟州区第一中学2021届高三下学期模拟检测二数学试题(已下线)第七章 导数与不等式能成立(有解)问题 专题四 双变量能成立(有解)问题的解法 微点1 双变量单函数能成立(有解)问题的解法(已下线)强化卷07(3月)-冲刺2020高考数学之拿高分题目强化卷(山东专版)
2019高一·全国·专题练习
7 . 已知函数
,方程
有四个不同的根,记最大的根的所有取值为集合
,若函数
有零点,则
的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91f5e417e640682e86553d320e720aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a18dd9bae0a40974235b4108995e6c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7909220d1db380634534190b662ee0a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc93d54b9a25284915034701317aed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0d90db48cf9da3e9c2e613fd0a86f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b61ed9fd6fbfbea7a406c80a7b92df8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
8 . 已知函数
(
)在其定义域内有两个不同的极值点.
(I)求a的取值范围;
(II)记两个极值点分别为
,且
.已知
,若不等式
恒成立,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5124251b521fb2525f55b99ee9ff6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(I)求a的取值范围;
(II)记两个极值点分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5def2e680848aaf69b5a8c0f50ce05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2016-12-04更新
|
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10卷引用:2016届辽宁省沈阳市高三教学质量监测一理科数学试卷
名校
解题方法
9 . 若函数
为定义域
上单调函数,且存在区间
(其中
),使得当
时,
的取值范围恰为
,则称函数
是D上的正函数,区间
叫做等域区间.
(1)是否存在实数m,使得函数
是
上的正函数?若存在,请求出实数m的取值范围;若不存在,请说明理由.
(2)若
,且不等式
的解集恰为
,求函数
的解析式.并判断
是否为函数
的等域区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0195f699765021e2c6ea985e487971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e207cf62e3a7e282eac4c4a3455bbf9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
(1)是否存在实数m,使得函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff0bea1f5a5fb07e1b75796fd9966b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574e5f7e33a62cf3d3df853742374a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d6042155c8df794673e780cfd420ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5b6b8572945a8ac7db96a26d5e8311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
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2023-09-07更新
|
712次组卷
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3卷引用:第三章 函数的概念与性质-【优化数学】单元测试能力卷(人教A版2019)
(已下线)第三章 函数的概念与性质-【优化数学】单元测试能力卷(人教A版2019)江苏省南通市海安高级中学2023-2024学年高三上学期阶段测试(一)数学试题山东师范大学附属中学幸福柳分校2023-2024学年高一上学期期中考试数学试题
名校
解题方法
10 . 已知函数
给出下列四个结论:
①若
有最小值,则
的取值范围是
;
②当
时,若
无实根,则
的取值范围是
;
③当
时,不等式
的解集为
;
④当
时,若存在
,满足
,则
.
其中,所有正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff4e0cfa86f6d91ff0b3cdb3251393b.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6cc71d0c988d725b25c55c2672919c.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976d18a5396ba232f0aa38d136f1d749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1606791e5eeefbf298210543e01dd4.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5bcfb3bafe8373dd907e0e55d08f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168fef6477a494abceae56fb6c2e4c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b61bb7cb94b4d06f0090df1e365667.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/339de01d9636343c484391b421c31301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec808ad60dbf016632ec816eaca1df.png)
其中,所有正确结论的序号为
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2023-11-02更新
|
825次组卷
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5卷引用:北京市第一零一中学2024届高三上学期10月月考数学试题