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Need help factoring in two variables

  1. Sep 17, 2011 #1
    1. The problem statement, all variables and given/known data

    Trying to find relative min/max

    2. Relevant equations


    3. The attempt at a solution

    partial WRT(x) = 4x^3-36y
    partial WRT(y) = 4y^3-36x

    Set Partial WRT(x) = 0


    plug x into Partial


    Im not sure what to do now to find the critical points?
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 17, 2011 #2
    Let ∂f/∂x=0 and ∂f/∂y=0.

    From your original post, you have

    ∂f/∂x = 4x3-36y = 4(x3-9y) = 0
    ∂f/∂y = 4y3-36x = 4(y3-9x) = 0

    Now all you have left to do is to find all points that satisfy both equations. Two equations. Two unknowns. Algebra holds the answer. o_O
    Last edited: Sep 17, 2011
  4. Sep 17, 2011 #3


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    Homework Helper

    You just plugged your solution for WRT(x) back into the equation WRT(x). You aren't going to get anything out of that. Try solving the WRT(x) equation for y and putting that into the WRT(y) equation. You'll get an equation of high degree, but it's pretty easy to say what the possible real roots are.
  5. Sep 17, 2011 #4
    Thanks for help
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