1 . 设函数
,那么f(x)的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6196d0217ab1a79183c118044745adc.png)
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2010高三·山东·竞赛
2 . 已知函数
在其定义域内既有极大值又有极小值. 则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960535f22d045df969f57d64e3d7673c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
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2008高三·山东·竞赛
3 .
为一定点,
是
轴上的一动点,点
满足
.若点
满足
,求:
(1)点
的轨迹曲线
的方程;
(2)曲线
的任何两条相互垂直的切线的交点轨迹.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1208e24cb1d3ae6a50f161b970ec2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d811e3371b79f5bd7a816acfa3aa4d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e48f79069ada435c8225a124f149c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e751487e28612c4d5c75cdc99cbb02f9.png)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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4 . 如图,由沿河城市
运货到另一地点
.
离河岸最近的
处
.按沿河的距离算,
的距离为
.如果水路运费是公路运费
(
是大于1的实数),欲从点
修一条公路到河岸点
处,为使由
到
的总运费最小,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d57b4243fa7f6f9c73d11f3123c42ddb.png)
______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d25a880079465f9d55e5874420d8d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69218441ce7f881590be5cad324353b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d57b4243fa7f6f9c73d11f3123c42ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce89b633e5d6bcf9406e3f9208fe06d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/a2fe1287-c85f-45f3-a923-2f998962642c.png?resizew=156)
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5 . 求直角坐标平面
上的点集
{
为R上单调函数,且
}所成图形的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add507c54e79434e18c4e0c79ee702e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447a9718a502491b47072ce013c26a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e308bcfae60eacf17af2c774d8e8f5ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a380067a20c25338eb0312e8df6c2760.png)
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6 . 设t为正数,数列
是首项为t,公差为2t的等差数列,其前n项和为
,若
,则t的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70d4081b340d8846cddb48a01e7de6cb.png)
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2003高三·山东·竞赛
7 . 已知
,函数
的图像按向量OA平移得到的图像恰与直线
相切于点
,则原函数的解析式是.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d562c9664e8b5c8504f818db10864e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e59da5115d0dafea24822245f92c48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd3df60003be782722f5e1811cf7876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79889b6d1d25749f38f0d0c7a4e8101.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2003高三·山东·竞赛
8 . 若p、q为实数,则函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60ff0d863bc08fd7810d67951633a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60ff0d863bc08fd7810d67951633a63.png)
A.在![]() | B.在![]() |
C.当![]() ![]() | D.当![]() ![]() |
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2012高三·山东·竞赛
9 . 函数
的单调递减区间为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f0a49cba17a64c151939ae43144d5c.png)
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