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Homework Help: Multivariable saddle point

  1. Jan 2, 2012 #1
    1. The problem statement, all variables and given/known data

    Find and classify all relative extrema and saddle points of the function
    f(x; y) = xy - x^3 - y^2.

    2. Relevant equations

    D = fxx *fyy -fxy^2

    3. The attempt at a solution

    I got D < 0 where D = -1 and fxx = 0, when x=0 and y=0. However I am unsure as to the conclusion I should arrive at when D < 0 but fxx = 0. I'm thinking that this is a saddle point?

    Thanks for the help in advance,
  2. jcsd
  3. Jan 2, 2012 #2


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    You need to find locations where both of the 1st partial derivatives are zero.
  4. Jan 2, 2012 #3
    yep those two pts are

    x=0, y=0
    x=1/6 y=1/12
  5. Jan 2, 2012 #4
    evaluating pt 0,0 I get D<0 where D= -1 and fxx(0,0) = 0, so then this is a saddle point. However is it a saddle point because D<0 or because fxx = 0?
  6. Jan 2, 2012 #5
    guess ur doing mab127 too

    when d < 0 its a saddle point doesnt matter what fxx is
  7. Jan 2, 2012 #6
    haha yep :D, thanks for the help.
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