1 . 已知函数f(x)=ax2-2x+1.
(1)试讨论函数f(x)的单调性;
(2)若
≤a≤1,且f(x)在[1,3]上的最大值为M(a),最小值为N(a),令g(a)=M(a)-N(a),求g(a)的表达式;
(3)在(2)的条件下,求证:g(a)≥
.
(1)试讨论函数f(x)的单调性;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(3)在(2)的条件下,求证:g(a)≥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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2 . 设
是实数,函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae6633cc8186766bb46f5e46e0254a5.png)
.
(1)求证:函数
不是奇函数;
(2)当
时,解关于
的不等式
;
(3)求函数
的值域(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae6633cc8186766bb46f5e46e0254a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3210274e57cc0487a58b99ea274b8aa1.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d3db25341ea76852ad7856c338df1c.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
3 . 已知函数
(
为实常数且
).
(Ⅰ)当
时;
①设
,判断函数
的奇偶性,并说明理由;
②求证:函数
在
上是增函数;
(Ⅱ)设集合
,若
,求
的取值范围(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99fcef3856a1d67acab12b85b5a4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da67075d5f20954afe0232112e159ac9.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd88b374924344fb157a15c2d36edad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
②求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9006ed5e53e4637fbacec7832dfe2146.png)
(Ⅱ)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d56bb1ee8639cb81434e10cb3c9a0cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4815b1d16a7ae485ff0bba0b397e893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
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2018-11-01更新
|
845次组卷
|
4卷引用:浙江省金华市第一中学2021-2022学年高一上学期期中数学试题
浙江省金华市第一中学2021-2022学年高一上学期期中数学试题(已下线)专练29 期中综合检测AB卷-2021-2022学年高一数学上册同步课后专练(人版A版2019必修第一册)【全国百强校】江西省新余市第四中学2018-2019学年高一10月月考数学试题浙江省2016年4月普通高中学业水平考试数学试题
名校
4 . 已知二次函数
,设方程
的两个实数根为
和
.
如果
,设二次函数
的对称轴为
,求证:
;
如果
,
,求b的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611957a07b6fc69e62f429b94a0bad0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f563b3277f2fc80e46baf9aa7070d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040135d64192de075ba0cc9f11ddbc9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa33c2bd791339d32821077846605d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2b81cdcc945ec5da0df9b502d9e903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05cbed9e2911c9fc7972d958f34b7148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50aa1911eba92e1fd9a99faca5ecf434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b0d1aac8e2a999eafb2a5409ad1c83f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f78c3bfa830b49b425e8eae3145225.png)
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2018-07-31更新
|
575次组卷
|
4卷引用:2015-2016学年江西铅山一中 、横峰中学高二上学期期中理科数学卷
名校
5 . 在平面直角坐标系中,O为坐标原点,A、B、C三点满足
.
求证:A、B、C三点共线;
已知
、
,
,
的最小值为5,求实数m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431d15b80cc65e037b35bc10bd8d45e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6611c73064bda197766c00b448dd0030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f8c513fdf6f75cdd4f441e35ecfc04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a848eab8a7cd5094a8dc37f9b91f38b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a39a25091e39b138526e12a3937872.png)
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2018-03-02更新
|
1941次组卷
|
9卷引用:湖北省宜昌市第二中学2018-2019学年高一下学期期中数学试题
名校
6 . 已知函数
.
(1)求证:函数
是偶函数;
(2)设
,求关于
的函数
在
时的值域
的表达式;
(3)若关于
的不等式
在
时恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e1c34e767abf34e4e1c1a4e41877ca.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c673cf6607904e539e0dbc43d5ddb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475b5daeeeb6e6bb4885904d131f9902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a7b7c834d06f3e28a339db94690172.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66282028f87237a5dc0bebb7ae338af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b2d0097fd22ccd9298a9e57e47dadc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2018-01-20更新
|
1218次组卷
|
4卷引用:上海市鲁迅中学2018-2019学年高三上学期期中数学试题
名校
解题方法
7 . 已知函数
.
(1)若任意
,不等式
恒成立,求实数
的取值范围;
(2)求证:对任意
,
,都有
成立;
(3)对于给定的正数
,有一个最大的正数
,使得整个区间
上,不等式
恒成立,求出
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8326d9b0e018962618d9d42aebed290a.png)
(1)若任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79c8048b437627dc13ab8c102539a4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a9f7884d2a1a1f304d8d468d8dd47c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求证:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bf60c5e8996d138198fe74f30ce520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9425f7c0d79b5de76946d89328844e.png)
(3)对于给定的正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a239d924a26dbc7f33052c63a20a327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1ff2f77455fed362050d679abce5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbabb741f7e5ef0d5bf7e5ee1c1ac67e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a239d924a26dbc7f33052c63a20a327a.png)
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名校
解题方法
8 . 已知二次函数
和一次函数
,其中
且满足
,
.
(1)证明:函数
与
的图像交于不同的两点;
(2)若函数
在[2,3]上的最小值为9,最大值为21,试求
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bd0587f5d6a3b5db9e4a93e0dbc0ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4f400ad3ab773b59cb89f36ce71976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0e9d1ad9561d693958756ee8398218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196be101149acfb6a6c4ceca7fc96828.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3c2be7482719651bcf491949681e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2016-12-04更新
|
553次组卷
|
4卷引用:天津市耀华中学2022-2023学年高一上学期期中数学试题
天津市耀华中学2022-2023学年高一上学期期中数学试题2016-2017学年河北武邑中学高一上周考9.11数学试卷(已下线)第二章 一元二次函数、方程和不等式(压轴必刷30题4种题型专项训练)-【满分全攻略】(人教A版2019必修第一册)(已下线)期中真题必刷压轴60题(15个考点专练)-【满分全攻略】(人教A版2019必修第一册)
解题方法
9 . 已知函数
为偶函数,关于
的方程
的构成集合
.
(1)求![](https://img.xkw.com/dksih/QBM/2016/1/13/1572435229065216/1572435234832384/STEM/a4f8d8bbb3374c1eb7aaf74559fe7284.png)
的值;
(2)若
,求证:
;
(3)设
,若存在实数
使得
,求实数
的取值范围.
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572435229065216/1572435234832384/STEM/959a0af83a4b4114b38e57fec4e6834e.png)
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572435229065216/1572435234832384/STEM/3a3e422d07824b33a44f2c4586bcfb7b.png)
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572435229065216/1572435234832384/STEM/e71521fa88aa4da585c7b7f2483a3ae8.png)
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572435229065216/1572435234832384/STEM/67062d53a2434f53bf4eeea8a4f519a5.png)
(1)求
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572435229065216/1572435234832384/STEM/a4f8d8bbb3374c1eb7aaf74559fe7284.png)
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572435229065216/1572435234832384/STEM/9327cadd37b24f3e99f49cb270777bdf.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572435229065216/1572435234832384/STEM/b8927464ad0e4c3bba6e8c2464a22179.png)
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572435229065216/1572435234832384/STEM/48454cc5a0cd4956a9c788529e34727c.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f0c4c7714099b5bafdb35d7ca146c8.png)
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572435229065216/1572435234832384/STEM/f3a8c6ecbd554aea86d405d279415fe0.png)
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572435229065216/1572435234832384/STEM/e73b7562ec07461db83271fe7bdd975c.png)
![](https://img.xkw.com/dksih/QBM/2016/1/13/1572435229065216/1572435234832384/STEM/5042f0287e4f4621be80c7f859834a9b.png)
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12-13高一上·北京·期中
10 . 定义在
上的函数
,如果满足:对任意
,存在常数
,都有
成立,则称
是
上的有界函数,其中
称为函数
的上界.
(1)判断函数
是否是有界函数,请写出详细判断过程;
(2)试证明:设
,若
在
上分别以
为上界,求证:函数
在
上以
为上界;
(3)若函数
在
上是以
为上界的有界函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea232de27d21a2646fd4520ea0726bf.png)
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ee2d6f5c82efb89f3ebe7857bbe19.png)
(2)试证明:设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd7bba058b2e191718d59debbe97a73f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aae37cac299cbe3ccac181b2175287f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae0f8520349250a31be6d58542ef2d9.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a18264722215b39ab53a098fd18bded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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