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Math Help - Maxima proof

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    9

    Maxima proof

    Hello!
    I have a question I'm struggling with, my last question was answered so helpfully I thought I'd try my others out here! Especially since my exam is in less than 3 hours!

    Its a 'Two variable function Extrema' question

    Q: The gravitational attraction at the point (x,y)=(1/x)+(4/y)+(9/(4-x-y))
    Prove that G(x,y) has a maximum value of 9

    These type of questions always stump me, sorry.

    Thanks for any aid
    Last edited by Chris9620; October 29th 2009 at 01:11 AM.
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  2. #2
    Senior Member
    Joined
    Apr 2009
    From
    Atlanta, GA
    Posts
    409

    Stump?

    I can see why it stumped you. First, how did the exam go? Second, this function has no maximum (or minimum), local or absolute.

    G(x,y)=\frac1x+\frac4y+\frac9{4-x-y}

    Consider: \lim_{x+y\to 4}G(x,y)=\pm\infty and \lim_{x,y\to\infty}G(x,y)=0 because of the \frac9{4-x-y} term.

    For traditional proof, \bigtriangledown G=\vec{0} has no solution.
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