Explore BrainMass

Explore BrainMass

    Four stationary points of a multivariable function

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    A surface is described by the multivariable function f(x,y) where:

    f(x,y) = x^3 + y^3 + 9(x^2 + y^2) + 12xy

    a) Show that the four stationary points of this function are located at:

    (x1, y1) = (0, 0)
    (x2, y2) = (-10, -10)
    (x3, y3) = (-4, 2)
    (x4, y4) = (2, -4)

    © BrainMass Inc. brainmass.com March 4, 2021, 5:36 pm ad1c9bdddf
    https://brainmass.com/math/computing-values-of-functions/four-stationary-points-multivariable-function-2311

    Solution Preview

    Stationary points are the points such that the partial derivatives of f(x,y) both with respect to x and y are 0.

    Take the partial derivative of f(x,y) both respect to x and y to get

    3x^2+18x+12y=0 (1)
    3y^2+18y+12x=0 ...

    Solution Summary

    This shows how to find the four stationary points of a function.

    $2.49

    ADVERTISEMENT