Results 1 to 2 of 2

Math Help - relative maxima and minima in a closed region

  1. #1
    Newbie
    Joined
    Feb 2013
    From
    canada
    Posts
    11

    relative maxima and minima in a closed region

    I'm working on a problem and it requires the relative maxima and minima of a closed region, I understand how to find the rel(max/min) of a function f(x,y) without the closed region(using fx, fy,fxy,fxx,fxy). Does anyone know how to do it with a closed region(ex circle x^2 + y^2 <= 1). Does it mean that all points outside of the circle I do not need to examine?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: relative maxima and minima in a closed region

    One trick I've seen used for a circular boundary is to parametrize the boundary so that you have one variable with which to work.

    In order to examine f on the boudary of the region, we represent the circle x^2+y^2=1 by means of the parametric equations x=\cos(t),\,y=\sin(t),\,0\le t\le2\pi. Thus, on the boundary we can write f as a function of a single variable t:

    f(t)=f(\cos(t),\sin(t))
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. maxima / minima
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 8th 2011, 06:03 AM
  2. Maxima And minima
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 11th 2009, 12:17 PM
  3. maxima and minima
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 25th 2008, 10:28 AM
  4. Maxima and minima
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 3rd 2007, 11:45 PM
  5. maxima and minima of f(x,y,z)
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 24th 2006, 12:31 AM

Search Tags


/mathhelpforum @mathhelpforum