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Find and classify all local minima, local maxima, and saddle points of the function f(x,y)= -3yx^2-3xy^2+36xy

  • cal3 -

    F = -3yx^2-3xy^2+36xy
    Fx = -6xy - 3y^2 + 36y
    Fxx = -6y

    Fy = -3x^2 - 6xy + 36x
    Fyy = -6x

    Fxy = -6x - 6y + 36

    D = FxxFyy-(Fxy)^2 = 36xy - 36(x+y-6)^2

    Fx = 0 Fy=0 at (0,0)
    D<0 so a saddle point


    Fx = -6xy - 3y^2 + 36y
    Fx = 0 when y = 2(6-x)

    Fy = -3x^2 - 6xy + 36x
    Fy = 0 when x = 2(6-y)

    So there is a local max for z along those two lines

  • cal3 -

    Okay Im just confused as how to get Fx=0 and Fy=0, If I set -6xy-3y^2+36y=0 how do i solve this?? Algebra was so long ago!
    could you detail that part of the problem...

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