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