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Homework Help: Proof of stationary points of 3D function

  1. Dec 28, 2011 #1
    1. The problem statement, all variables and given/known data

    Show that f(x,y)=g(x,y)h(x,y) is stationary if and only if:
    g=0 and h=0
    df/dx=0 and (dg/dx)(dh/dy)=(dg/dy)(dh/dx)
    (All the d's in the line above should be curly d's for partial derivatives.)

    2. Relevant equations

    3. The attempt at a solution

    I tried expressing df as a total derivative then setting this equal to zero, but I wasn't getting anywhere.
  2. jcsd
  3. Dec 28, 2011 #2
    Any suggestions would be great. :)
  4. Dec 28, 2011 #3


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    Science Advisor
    Homework Helper

    f is stationary if df/dx=0 and df/dy=0 (the d's being partial derivatives). g=0 and h=0 are certainly sufficient to show that. Just use the product rule. Where did you go from there? Can you show your work? Use that one of g or h must be nonzero.
    Last edited: Dec 28, 2011
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