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Maximizing the function

  1. Jun 11, 2007 #1
    The problem statement, all variables and given/known data

    Maximize the function f(x,y) = x^2y constrained by the circle x^2 + y^2 = 12





    The attempt at a solution

    I already went as far as solving lambda in my work; however, it's still a variable so I could not plug it in to solve for x and y.

    http://img.photobucket.com/albums/v407/dazedoutpinoy/Calculus001.jpg
     
  2. jcsd
  3. Jun 12, 2007 #2
    (it took me a while to understand the meaning of (i) and (j), ...)

    From the two equations you have writen, you can now eleminate lambda.
    In this way, you will get a curve (two lines actually) where the gradient of f is perpendicular to circles centered on the origin.
    (Df = lambda Dg means that as you know: the gradient of f should have no finite component along the given circle)

    Then, you should simply find out the intersection of this curve with the particular circle you are targeting.
     
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