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December 16th, 2008, 08:39 AM   #1
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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:

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December 16th, 2008, 10:19 AM   #2
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Re: Extremum

There is a theorem for twice-differentiable 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.)
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December 16th, 2008, 10:25 AM   #3
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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
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Re: Extremum

Thank you You are really helpful guys
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