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Calculus/differential calculus applications

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Expert: - 6/22/2008


Question
what is meant by critical point,stationary point,absolute maximum,local maximum,absolute minimum,local minimum.
how will i calculate all the above in the function f(x)=2-3x.x

Answer
A critical point is any of the following:
I don't know what is meant by a, 'staitionary point'.
Absolute max: max over the interval specified,
Absolute min: min over the interval specified,
Local max: max in the area, and
Local min: min in the area.

Is that function suppose to be 2-3x*x?  The derivative is -3x^2.  This is 0 at x=0.  The second derivative is -3, which is negative, which implies that this must be a maximum.
The local and absolute max is at x=0.  The min's are at the endpoints on either side of 0.  If there are no endpoints, the mins are at x equal plus infinit and minus infinity.
The abosolute max and min again depend on if you have any endpoints in the x values to work with, like x>=-4 or -10<=x<=6.  

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