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Critical Points - Multivariable Calc

  1. Nov 7, 2009 #1
    Hi, i was wondering if someone could please help to find and classify the critical points of :
    f(x,y) = (x-y)^2

    What i know:
    I got fx = 2(x-y) and fy = -2(x-y)
    and in order to find the critical points we need to solve:

    2(x-y) =0
    -2(x-y) = 0

    so if x =y then the above hold.

    where would I go on from here on?

    Last edited: Nov 7, 2009
  2. jcsd
  3. Nov 8, 2009 #2


    User Avatar

    Basically anything that runs along the line y=x would contain your critical points. Plug y=x into the hessian matrix and then determine what kind of extrema it is.
  4. Nov 8, 2009 #3
    Alright! thanks a lot :D
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