December 16th, 2008, 08:39 AM  #1 
Newbie Joined: Dec 2008 Posts: 26 Thanks: 0  Extremum
I've got another interesting (I hope) problem and I hope you'll help me to solve it Well it goes like this: Determine all points, where function f has it's extremums, and define whether it is maximum or minimum, if: 
December 16th, 2008, 10:19 AM  #2 
Senior Member Joined: Dec 2008 Posts: 251 Thanks: 0  Re: Extremum
There is a theorem for twicedifferentiable functions f(x, y) that if at at at then f(x, y) has a relative maximum at (x, y), and similarly a relative minimum if . (I believe it can be proved with Taylor's theorem.) 
December 16th, 2008, 10:25 AM  #3 
Guest Joined: Posts: n/a Thanks:  Re: Extremum
Think about partial derivatives. ...[1] ...[2] Set each to 0. Solve [1] for y and sub into [2]. Then, solve for x. You can get y by subbing the x's back into the y you found. Check the critical points by using the second partials derivative test. It can be found in any calc book. 
December 16th, 2008, 11:13 AM  #4 
Newbie Joined: Dec 2008 Posts: 26 Thanks: 0  Re: Extremum
Thank you You are really helpful guys 

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