已知函数f(x)=x
3+ax
2+bx.
(1)若函数y=f(x)在x=2处有极值-6,求y=f(x)的单调递减区间;
(2)若y=f(x)的导数f′(x)对x∈[-1,1]都有f′(x)≤2,求
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的范围.
考点分析:
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抛物线y
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1:y=x和l
2:y=-x相切的圆.
(1)求定点N的坐标;
(2)是否存在一条直线l同时满足下列条件:
①l分别与直线l
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2交于A、B两点,且AB中点为E(4,1);
②l被圆N截得的弦长为2.
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设数列{b
n}的前n项和为S
n,且b
n=2-2S
n;数列{a
n}为等差数列,且a
5=14,a
7=20.
(1)求数列{b
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已知平面直角坐标系
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,圆C是△OAB的外接圆.
(1)求圆C的方程;
(2)若过点(2,6)的直线l被圆C所截得的弦长为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182646104363557/SYS201310241826461043635016_ST/1.png)
,求直线l的方程.
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如图所示,在棱长为2的正方体ABCD-A
1B
1C
1D
1中,E、F分别为DD
1、DB的中点.
(1)求证:EF∥平面ABC
1D
1;
(2)求证:EF⊥B
1C;
(3)求三棱锥
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的体积.
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已知向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182646104363557/SYS201310241826461043635014_ST/0.png)
=(cos
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,sin
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),
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182646104363557/SYS201310241826461043635014_ST/3.png)
=(cos
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,-sin
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),
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182646104363557/SYS201310241826461043635014_ST/6.png)
=(
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,-1),其中x∈R.
(I)当
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⊥
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时,求x值的集合;
(Ⅱ)求|
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-
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|的最大值.
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