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Using the Second Partials Test

Find the relative extrema of f(x,y)=-x^(3)+4xy-2y^(2)+1

  • cal -

    fx = 3 x^2 + 4 y
    level if x = +/-(4y/3)^.5
    fxx = 6 x
    fxy = 4

    fy = 4 x - 4 y level when x = y
    fyy = -4
    fyx = 4

    extreme only when x = y = 0

    H matrix

    6 x 4
    4 -4

    det = -6x - 4
    if x = 0, det = -4
    if det <0 then (0,0) is a "saddle point"

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