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函数f(x)满足f(0)=0,其导函数f′(x)的图象如图,则f(x)的图象与x...
函数f(x)满足f(0)=0,其导函数f′(x)的图象如图,则f(x)的图象与x轴所围成的封闭图形的面积为( )
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123704043320366/SYS201310251237040433203004_ST/images0.png)
A.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123704043320366/SYS201310251237040433203004_ST/0.png)
B.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123704043320366/SYS201310251237040433203004_ST/1.png)
C.2
D.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123704043320366/SYS201310251237040433203004_ST/2.png)
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设a∈R,函数f(x)=e
x+a•e
-x的导函数是f′(x),且f′(x)是奇函数.若曲线y=f(x)的一条切线的斜率是
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,则切点的横坐标为( )
A.ln2
B.-ln2
C.
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D.
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已知b>a,下列值:∫
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f(x)dx,∫
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|f(x)|dx,|∫
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|的大小关系为( )
A.|∫
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|≥∫
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|f(x)|dx≥∫
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f(x)d
B.∫
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|f(x)|dx≥|∫
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f(x)dx|≥∫
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f(x)d
C.∫
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|f(x)|dx=|∫
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f(x)dx|=∫
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123704043320366/SYS201310251237040433203002_ST/11.png)
f(x)d
D.∫
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|f(x)|dx=|∫
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f(x)dx|≥∫
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f(x)d
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若在曲线f(x,y)=0(或y=f(x))上两个不同点处的切线重合,则称这条切线为曲线f(x,y)=0或y=f(x)的“自公切线”.下列方程:
①x
2-y
2=1;
②y=x
2-|x|;
③y=3sinx+4cosx;
④|x|+1=
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对应的曲线中存在“自公切线”的有( )
A.①③
B.①④
C.②③
D.②④
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曲线y=
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与直线y=x-1及x=4所围成的封闭图形的面积为( )
A.2-ln2
B.4-21n2
C.4-ln2
D.21n2
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已知三次函数f(x)=ax
3+bx
2+cx(a,b,c∈R).
(1)若函数f(x)过点(-1,2)且在点(1,f(1))处的切线方程为y+2=0,求函数f(x)的解析式;
(2)当a=1时,若-2≤f(-1)≤1,-1≤f(1)≤3,试求f(2)的取值范围;
(3)对∀x∈[-1,1],都有|f′(x)|≤1,试求实数a的最大值,并求a取得最大值时f(x)的表达式.
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