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Math Help - Finding All Critical Points of f(x,y)

  1. #1
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    Question Finding All Critical Points of f(x,y)

    I'm having some trouble finding all the critical points of the following function.

    See figure attached for function and my work.

    How can I get the equation of the line that contains all those critical points?

    Thanks again!
    Attached Thumbnails Attached Thumbnails Finding All Critical Points of f(x,y)-cpq.jpg  
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  2. #2
    MHF Contributor harish21's Avatar
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    the first and second lines of your solution should be:

    f_{x} = 3x^2y^3 - 2xy^2 = xy^2(3xy-2)

    and f_{y}=3x^3y^2-2x^2y=x^2y(3xy-2)
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