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November 12th, 2010, 10:17 AM   #1
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infimum, supremum of two argument function in particular set

Here is the task:
Find supremum and infimum of , if .

I have tried two ways:
1) searching for partial derivatives in order to find local extrema, but here is what happens:

So, it means that there is no local extreme points at all? Or all are extreme points?
2) from D follows that . Then I can get function and look for extreme points of g(x).

How do you think? Which way could fit? Or am I wrong in both of them?
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November 12th, 2010, 11:26 AM   #2
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Re: infimum, supremum of two argument function in particular

\frac{\partial f}{\partial x}=2x+2y,
\frac{\partial f}{\partial y}=2x+2y
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November 12th, 2010, 02:54 PM   #3
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Re: infimum, supremum of two argument function in particular

You need to use Lagrange multipliers.

http://en.wikipedia.org/wiki/Lagrange_multipliers
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