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November 12th, 2010, 10:17 AM  #1 
Member Joined: Jan 2010 Posts: 44 Thanks: 0  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? 
November 12th, 2010, 11:26 AM  #2 
Member Joined: Jan 2010 Posts: 44 Thanks: 0  Re: infimum, supremum of two argument function in particular
\frac{\partial f}{\partial x}=2x+2y, \frac{\partial f}{\partial y}=2x+2y 
November 12th, 2010, 02:54 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,216 Thanks: 493  Re: infimum, supremum of two argument function in particular 

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