名校
1 . 已知定义在区间
上的函数
,其中常数
.
(1)若函数
分别在区间
上单调,试求
的取值范围;
(2)当
时,方程
有四个不相等的实根
.
①证明:
;
②是否存在实数
,使得函数
在区间
单调,且
的取值范围为
,若存在,求出
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c9eca1510647f9b40cf7ce69c3757f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26337502f8a07b4655416be99c2c09b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
(1)若函数
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792483540934656/1793041726971904/STEM/6318e0e1e1f84a3da44c6ac2c1beaef2.png?resizew=36)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e670e88873b35b46ad6d193d8a55e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16df3112ff53691d26bca57f85cdc3b.png)
②是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792483540934656/1793041726971904/STEM/6318e0e1e1f84a3da44c6ac2c1beaef2.png?resizew=36)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792483540934656/1793041726971904/STEM/6318e0e1e1f84a3da44c6ac2c1beaef2.png?resizew=36)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8af7bed124f00c8e19b52d028b4d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-12-03更新
|
1139次组卷
|
4卷引用:2015-2016学年湖北宜昌市一中高一上期中考试数学试卷
名校
2 . 如图,某广场为一半径为80米的半圆形区域,现准备在其一扇形区域
内建两个圆形花坛,该扇形的圆心角为变量
,其中半径较大的花坛
内切于扇形,半径较小的花坛
与
外切,且与
、
相切.
![](https://img.xkw.com/dksih/QBM/2015/11/24/1572302444544000/1572302450614272/STEM/c9b598cacb0a47f58a89e89f46070a7b.png?resizew=258)
(1)求半径较大的花坛
的半径(用
表示);
(2)求半径较小的花坛的半径
的最大值.
![](https://img.xkw.com/dksih/QBM/2015/11/24/1572302444544000/1572302450614272/STEM/780af53839bc401cbc14ed788056428d.png?resizew=36)
![](https://img.xkw.com/dksih/QBM/2015/11/24/1572302444544000/1572302450614272/STEM/1b91e72eb6aa45cb9caf9662dc25842c.png?resizew=100)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb52bba9798c625c7cd778636bceea32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://img.xkw.com/dksih/QBM/2015/11/24/1572302444544000/1572302450614272/STEM/95a71e11e29246ec8dfe68bc79fc709d.png?resizew=25)
![](https://img.xkw.com/dksih/QBM/2015/11/24/1572302444544000/1572302450614272/STEM/9288547aa89f4da1a2d3ba64e98e66d7.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2015/11/24/1572302444544000/1572302450614272/STEM/c9b598cacb0a47f58a89e89f46070a7b.png?resizew=258)
(1)求半径较大的花坛
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://img.xkw.com/dksih/QBM/2015/11/24/1572302444544000/1572302450614272/STEM/b6f6dd629fc64f47a1ebd2e623fcb53a.png?resizew=13)
(2)求半径较小的花坛的半径
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb52bba9798c625c7cd778636bceea32.png)
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2016-12-03更新
|
772次组卷
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2卷引用:2016届江苏省泰州中学高三上学期第二次月考理科数学试卷
解题方法
3 . 已知f(x)=
,
.
(1)若b≥1,求证:函数f(x)在(0,1)上是减函数;
(2)是否存在实数a,b,使f(x)同时满足下列两个条件:
①在(0,1)上是减函数,(1,+∞)上是增函数;
②f(x)的最小值是3.若存在,求出a,b的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78c8c3b4e6038f13d6bfe0fe4213c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0048e4b37ff9dee9712a48c528e6b1a.png)
(1)若b≥1,求证:函数f(x)在(0,1)上是减函数;
(2)是否存在实数a,b,使f(x)同时满足下列两个条件:
①在(0,1)上是减函数,(1,+∞)上是增函数;
②f(x)的最小值是3.若存在,求出a,b的值;若不存在,请说明理由.
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2016-12-03更新
|
372次组卷
|
3卷引用:2015-2016学年广东省东莞南开实验学校高一下学期期初考试数学试卷
名校
4 . 对于函数
,如果存在实数
使得
,那么称
为
的生成函数.
(1)下面给出两组函数,
是否分别为
的生成函数?并说明理由;
第一组:
;
,生成函数
.若不等式
在
上有解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c533ce6c0a48950039e7663481c68e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c974dafd7f992c28eb67787daa6387b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/456e886959387cd96195f4caabafe8c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e869b4f2bc6c79c274a4d94879ffdea.png)
(1)下面给出两组函数,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e869b4f2bc6c79c274a4d94879ffdea.png)
第一组:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d45bdbce78732d926295abd06a2f5b0.png)
第二组:;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d55b4b47f0b774ca47b7bd43fb05a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d5ec10000ab1785a704ec76cf1fa518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b97e73938ec09765c003e0a429059ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2016-12-03更新
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689次组卷
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7卷引用:2014-2015学年江苏省涟水县一中高一下学期期末调研数学试卷
名校
5 . 如图所示,公园内有一块边长为
的等边
形状的三角地,现修成草坪,图中
把草坪分成面积相等的两部分,
在
上,
在
上.
![](https://img.xkw.com/dksih/QBM/2015/10/10/1572256703840256/1572256710049792/STEM/83b013e487864fcfa2ca1392c514964d.png)
(Ⅰ)设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832a361da851b54c6437a96488a1b987.png)
,试用
表示
的函数关系式;
(Ⅱ)如果
是灌溉水管,为节约成本希望它最短,
的位置应该在哪里?如果
是参观线路,则希望它最长,
的位置又在哪里?请给予证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878e89b6eca35e34c863e832a2c661db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2015/10/10/1572256703840256/1572256710049792/STEM/83b013e487864fcfa2ca1392c514964d.png)
(Ⅰ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832a361da851b54c6437a96488a1b987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5d70e5d13db498f1c8a2e017c56e58b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(Ⅱ)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
您最近一年使用:0次
2016-12-03更新
|
715次组卷
|
3卷引用:2014-2015学年四川省新津中学高一6月月考数学试卷
6 . (如图,某海滨浴场的岸边可近似地看成直线,位于岸边A处的救生员发现海中B处有人求救,救生员没有直接从A处游向B处,而是沿岸边自A跑到距离B最近的D处,然后游向B处,若救生员在岸边的行进速度为6米/秒,在海中的行进速度为2米/秒,
.
![](https://img.xkw.com/dksih/QBM/2015/10/10/1572256485335040/1572256490700800/STEM/7be98468ace94235b7c7875617a40d91.png)
(1)分析救生员的选择是否正确;
(2)在AD上找一点C,使救生员从A到B的时间为最短,并求出最短时间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35a9e9bdb772c2f5172e0c5d514161d.png)
![](https://img.xkw.com/dksih/QBM/2015/10/10/1572256485335040/1572256490700800/STEM/7be98468ace94235b7c7875617a40d91.png)
(1)分析救生员的选择是否正确;
(2)在AD上找一点C,使救生员从A到B的时间为最短,并求出最短时间.
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7 . 设函数![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248902107136/1572248908193792/STEM/43d0a16dd7a641a387b332f0a792c728.png)
且
,当点
是函数
图象上的点时,点
是函数
图象上的点.
(1)写出函数
的解析式;
(2)若当
时,恒有
,试确定
的取值范围.
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248902107136/1572248908193792/STEM/43d0a16dd7a641a387b332f0a792c728.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248902107136/1572248908193792/STEM/295af38b645c445ab1438be783eea6c0.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248902107136/1572248908193792/STEM/13acda743f7c45679bd14602466b0fc2.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248902107136/1572248908193792/STEM/791e9be1a9624904bcfe5bb2e3f9bdf2.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248902107136/1572248908193792/STEM/e6cefb37778c497cb8551699013c3d85.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248902107136/1572248908193792/STEM/7a64b4aabce345278bc4642578058c1e.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248902107136/1572248908193792/STEM/8d1fec611e574ce390135cf456d5f7a8.png)
(1)写出函数
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248902107136/1572248908193792/STEM/8d1fec611e574ce390135cf456d5f7a8.png)
(2)若当
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248902107136/1572248908193792/STEM/ea0e34c1e8f84c39afb3ec09a964bf86.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248902107136/1572248908193792/STEM/793dbe54aa3d44f48b8170819784a1a5.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248902107136/1572248908193792/STEM/fd2d6d946c394f6a82f08e426567cf50.png)
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名校
8 . 如图,甲、乙两个企业的用电负荷量
关于投产持续时间
(单位:小时)的关系
均近似地满足函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a053eaf3bf332eda81b4ca7f1def31af.png)
.
![](https://img.xkw.com/dksih/QBM/2015/9/9/1572228154015744/1572228159946752/STEM/142da68a156d48568a07ceaae3d226e5.png)
(1)根据图象,求函数
的解析式;
(2)为使任意时刻两企业用电负荷量之和不超过
,现采用错峰用电的方式,让企业乙比企业甲推迟![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
小时投产,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9b65c51e37f40211b876be02105701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a053eaf3bf332eda81b4ca7f1def31af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff28398d3e654426729eaa0ff99ed4a9.png)
![](https://img.xkw.com/dksih/QBM/2015/9/9/1572228154015744/1572228159946752/STEM/142da68a156d48568a07ceaae3d226e5.png)
(1)根据图象,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c8ca569e742d9eeee3b85f61bd8e17.png)
(2)为使任意时刻两企业用电负荷量之和不超过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca74e3bfe66db258ab238ecf3b08b47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6fdb690a72e89bcacbe9e49885e2c79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
9 . 设函数
是定义域为R的奇函数
(Ⅰ)若
,试判断函数单调性并求使不等式
在定义域上恒成立的
的取值范围;
(Ⅱ)若
,且
在
,
上最小值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041622d72d3ba99cd15524da8617679e.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f54ecfa11026d97c8d315e55e0d34a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430ecadf733b60dbe173dd4ce8b5734.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c85886dad735d5b8048ba3d3eab4ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683a34e929399278f319421486390cd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f124fb9eab689c537bb5ddf5012e35f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7ddb5245cbaa046b6e554dcb540a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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10 . 已知函数
.
(Ⅰ)若
,求
的单调区间;
(Ⅱ)若
,且存在实数
满足
,
.设
的最大值为
,求
的取值范围(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/076ae2e81ab77afaf865e7292a69ade3.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51b766a19dea472fd6694a9b70d7e83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf105efd4cf5f580d0561e54d923e347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c5ebc202fe6ebf6c283b31e02f7244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0615c4a1072407f2e6422056760472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be837b55c392129d22e35a0b97921c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb708adff55a5bda517c3f570f06584c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb708adff55a5bda517c3f570f06584c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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