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Homework Help: Finding critical points

  1. Mar 6, 2008 #1
    1. The problem statement, all variables and given/known data

    Find and classify the critical points of f(x,y,z) = xy + xz + yz + x^3 + y^3 + z^3

    2. Relevant equations
    3. The attempt at a solution

    df/dx = y + z +3x^2, df/dy = x + z + 3y^2 and df/dz = x + y + 3z^2

    a point x is a critacal point if the gradient equals 0.

    Obviously (0,0,0) is a critical point but I´m not sure how to find the others.
  2. jcsd
  3. Mar 6, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi gassi! Welcome to PF! :smile:

    Hint: the whole problem is completely symmetric in x y and z, isn't it?

    So try adding or subtracting df/dx df/dy and df/dz. :smile:
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