1 . 已知二次函数
(
均为实数)满足
,对于任意实数
都有
,并且当
时,有
.
(1)求
的值;
(2)证明
;
(3)当
时,函数
(
为实数)是单调的,求证:
或
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331d5e308cd5469e0f28a8d75f79903f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a431537df789febf4bc45e3dc23cefaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5480f15ca0864627e652e67784fc4b07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58427d5aa7deeca47c8789241913f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e08b4f3fa330e70f9d28bc866b5ddc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8c25a0a31b41ea8aa9a8658af4953d.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6785823721fb2e288b417ba2d617ef04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a878fd5a7104a7f42770a19097d56457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d191d6de821fbb06a51b5a20112db6de.png)
您最近一年使用:0次
2021-08-23更新
|
82次组卷
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2卷引用:陕西省咸阳百灵学校2020-2021学年高二下学期第一次月考文科数学试题
名校
解题方法
2 . 设函数
(a,
);
(1)若
,求证:函数
的图像必过定点;
(2)若
,证明:
在区间
上的最大值
;
(3)存在实数a,使得当
时,
恒成立,求实数b的最大值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80027540415bd2b98c9be19e21b5f8d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b40b1544e62be8b9e9f4dc9f2c0c74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fedf88c1afae37dcb344708fa1918db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09a2b7c019dae83e027830b82b3ee8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2aa311daf7a73f8c45de4462f9d92b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5193a9a29c504059dcbecfb81ca496.png)
(3)存在实数a,使得当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42f54feac6ed738a868ecd53d3a85a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d9926ad419c75a83ca90457a1e2fc1.png)
您最近一年使用:0次
2020-02-10更新
|
257次组卷
|
2卷引用:浙江省浙北G2联盟(湖州中学、嘉兴一中)2021-2022学年高二下学期期中联考数学试题
名校
3 . 已知二次函数
(
均为实数),满足
,对于任意实数
都有
,并且当
时,有
.
(1)求
的值;并证明:
;
(2)当
且
取得最小值时,函数
(
为实数)单调递增,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bd0587f5d6a3b5db9e4a93e0dbc0ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c766352f0be38b719621052de92615bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fffcb16e0156bb695b6f97b5c654661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff133c17652425c22f0b367e002797df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd53e5d21d735d3d2dfb6ee01ec2650c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74156327e5659301f391814605688899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17d9b0379b2b27da73d525d61de9093.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75bde2e500fd5386e355db9040a1946d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1810555c0c28fe352841322b85bbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/461d9ebddd8fd839073485e9dc113256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434e938638cced59180fb39abbf78b95.png)
您最近一年使用:0次
2017-09-02更新
|
51次组卷
|
2卷引用:贵州省铜仁一中2016-2017学年高二下学期期末数学(文)试题
名校
4 . 在
中,内角
所对的边分别为
,满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c109fb5db5efdd7558fc14be27508f8.png)
(1)求证:
;
(2)若
为锐角三角形,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c109fb5db5efdd7558fc14be27508f8.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8904522bf844b61febddc24346f8232f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/824379180b91379b3cad7cfc3533be39.png)
您最近一年使用:0次
2023-12-11更新
|
912次组卷
|
5卷引用:湖南省邵阳市邵东市第一中学2023-2024学年高二下学期3月月考数学试题
湖南省邵阳市邵东市第一中学2023-2024学年高二下学期3月月考数学试题重庆市拔尖强基联盟2024届高三上学期12月月考数学试题(已下线)专题3-4解三角形大题综合归类-1(已下线)重难点专题05 三角形中的范围与最值问题-【帮课堂】(苏教版2019必修第二册)(已下线)黄金卷06
5 . 已知
,
(1)若函数
与
在
时有相同的值域,求
的取值范围;
(2)若方程
在
上有两个不同的根
,求
的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e14c2f347403fb0f36d1549d10ab9f4.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1d358875baefff9736f2f31c2e28e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae8b0843577a84645d1887c7136e9305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad80c4ba8c593c5edfb167ae4a5f50f5.png)
您最近一年使用:0次
6 . 已知函数
,
.
(1)若
是奇函数,求a的值并判断
的单调性(单调性不需证明);
(2)对任意
,总存在唯一的
,使得
成立,求正实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c064cd16c1c95023009c344564a1022a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad0bcb38bd67c085ab01b13cf7a3e05.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3715365d7cf7959b963815c32327c4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30a4750430b4b0e9daa3edbef242184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
您最近一年使用:0次
2023-06-12更新
|
1393次组卷
|
3卷引用:2023年6月浙江省学业水平适应性考试数学试题
名校
7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fb457bbf52098c578c6b467b0832fc.png)
(1)若函数
在区间
的值域为
,求
的值;
(2)令
,
(i)若
在
上恒成立,求证:
;
(ii)若对任意实数
,方程
恒有三个不等的实数根,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fb457bbf52098c578c6b467b0832fc.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8e0f430dce833dbdb0dab22f082545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8e0f430dce833dbdb0dab22f082545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28eb47bf11a209a6521e16bbed6cbdb.png)
(i)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6ec0c3b57cf29ecf13ab8f1b0238df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385d882db31ffd5a0261c0577ffda20e.png)
(ii)若对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4c79d578d4b0d74b84c3f6579e8806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50683751e9dcd7b55555b53785f61a0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-06-17更新
|
284次组卷
|
2卷引用:浙江省温州十校联合体2022-2023学年高二下学期期中联考数学试题
名校
8 . 已知函数
,
(1)当
时,求
的单调递减区间;
(2)若
有三个零点
,且
求证:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2934e598129330a50d421af214be94.png)
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c1d68a6733e0a4dd0d2dee412cd6e2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2934e598129330a50d421af214be94.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cddc8d981e864d9d5a86f3e2ae40a91.png)
您最近一年使用:0次
2023-06-22更新
|
358次组卷
|
3卷引用:浙江省杭州市临安中学2023-2024学年高二上学期开学考试数学试题
解题方法
9 . 已知函数
满足:①
的一个零点为2;②
的最大值为1;③对任意实数
都有
.
(1)求
,
,
的值;
(2)设函数
是定义域为
的单调增函数,且
.当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331d5e308cd5469e0f28a8d75f79903f.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d73d9aa53e2d496bb14e106d82289940.png)
(1)求
![](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/071a7e733d466949ac935b4b8ee8d183.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd990aa73c80408442e42d611ae50534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efede742f4fd5b0a50d295bf403299f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df4d81ab50aabe801e40f85df0ada739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/359e95e435df82fd6f29e17348119581.png)
您最近一年使用:0次
解题方法
10 . 已知函数
,
.
(1)当
,求a;
(2)当
在
上单调递增,问a的取值范围;
(3)设
为
和
中的较小者,证明
在
上的最大值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ede4a660ea4ec1bac8834a388f54a69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eb2613dda00677d447c986cac505bc.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27fd67d7f50b6d6d6f8cf4cc58b3e55b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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