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Finding min's and max's in 3D

  1. Dec 4, 2005 #1

    Pengwuino

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    Hey guys im very confused here.. I have no idea how to do this! I need to find the max/mins of this equation and I get lost after finding the partials.

    [tex] f(x,y) = xy(1 - x - y) \\ [/tex]
    [tex] f_x (x,y) = y - 2xy - y^2 \\ [/tex]
    [tex] f_y (x,y) = x - x^2 - 2xy \\ [/tex]

    I know I'm suppose to kinda do what you do with single variables... but im getting lost with these multivariables... any help would be very much appreciated :)
     
  2. jcsd
  3. Dec 4, 2005 #2

    Tide

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    To find relative extrema set the gradient of the function to zero. Once you've found candidates, you'll need to determine whether the points are minima, maxima or saddle points.
     
  4. Dec 4, 2005 #3

    Pengwuino

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    that doesn't seem like how we were being taught in the book. It seemed like they were doing it all algebraicly
     
  5. Dec 5, 2005 #4

    benorin

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    more simply: set [tex]f_{x}=f_{y}=0[/tex] and solve the system for x and y
     
  6. Dec 5, 2005 #5

    Tide

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    IOW, like benorin said, set the derivatives equal to zero.
     
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