Results 1 to 4 of 4

Math Help - infimum and supremum of two argument function in particular set

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    53

    infimum and supremum of two argument function in particular set

    Here is the task:
    Find supremum and infimum of f(x,y)=x^2+2xy+y^2, if (x,y)\in D, D=\{(x,y)\mid 6x^2+y^2-1=0\}.

    I have tried two ways:
    1) searching for partial derivatives in order to find local extrema, but here is what happens:
    \frac{\partial f}{\partial x}=2x+2y, <br />
\frac{\partial f}{\partial y}=2x+2y
    So, it means that there is no local extreme points at all? Or all (x,y)\mid x=-y are extreme points?
    2) from D follows that y=\pm \sqrt(1-6x^2). Then I can get function g(x)=f(x,\pm\sqrt(1-6x^2)) and look for extreme points of g(x).

    How do you think? Which way could fit? Or am I wrong in both of them?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member roninpro's Avatar
    Joined
    Nov 2009
    Posts
    485
    Have you considered using Lagrange Multipliers?

    Pauls Online Notes : Calculus III - Lagrange Multipliers
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2010
    Posts
    53
    Frankly, I haven't. Now when you mention it, I guess that we have used this method in Economics, unfortunately without proof. Checked the link you added and it seems that it will work for me. Thank you!

    But how do you think about my actions before? Unnecessary?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member roninpro's Avatar
    Joined
    Nov 2009
    Posts
    485
    I think that it works - it's just painful.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. supremum and infimum
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: December 4th 2010, 06:32 PM
  2. supremum infimum
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 12th 2010, 05:40 AM
  3. Supremum and infimum
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 19th 2010, 04:16 AM
  4. Supremum and infimum
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: September 17th 2010, 06:29 PM
  5. supremum and infimum
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 24th 2007, 05:46 PM

Search Tags


/mathhelpforum @mathhelpforum