March 18th, 2012, 05:04 PM  #1 
Senior Member Joined: Jan 2010 Posts: 324 Thanks: 0  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? 
March 18th, 2012, 06:14 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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] 
March 20th, 2012, 08:34 PM  #3 
Senior Member Joined: Jan 2010 Posts: 324 Thanks: 0  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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extrema, finding, points, values 
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