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March 18th, 2012, 05:04 PM   #1
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Finding extrema points and values

So we have a function F(x,y) such that x^3+3xy+y^3 on the domain formed by -2<=x<=2 and -2<=y<=2
he wants us to find the criticle points and have the coordinates and function values..

wanna help me out with this?
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March 18th, 2012, 06:14 PM   #2
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Re: Finding extreema points and values

The first partial derivatives are:

and

Equating both to zero implies that we have the critical points:

(0,0), (-1,-1)

To determine whether extrema exist at these points, we may employ the second partials test:

Let

First point:



This point is not an extremum.

Second point:





This point is a relative maximum. The local maximum has a value of:



Here is a 3D plot with contour lines:

[attachment=0:1a7k5mr3]3dplot.jpg[/attachment:1a7k5mr3]
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March 20th, 2012, 08:34 PM   #3
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Re: Finding extrema points and values

He gave us a list of ten points though. like (0,0) .... (-sqrt 2, -2)...etc.
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