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Critical points with multiple variables

  1. Jun 5, 2012 #1
    1. The problem statement, all variables and given/known data

    Locate and classify the critical points of f(x,y) = (x-y)(xy-1).

    2. Relevant equations

    3. The attempt at a solution

    I found the partial derivatives with respect to x and y and I got:

    ∂f/∂x = -y2+2xy-1 ∂f/∂y = x2-2xy+1

    After setting them both equal to zero I can't find a way to solve for x and y.
  2. jcsd
  3. Jun 5, 2012 #2


    Staff: Mentor

    So your equations are y2 - 2xy +1 = 0 and x2 - 2xy + 1 = 0.

    Or y2 = 2xy -1, and x2 = 2xy - 1.

    Can you continue from here?
  4. Jun 5, 2012 #3
    wow, yes, thank you :redface: this is what happens when you do too many of these problems in one night
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