1. The problem statement, all variables and given/known data Find the four stationary points of the function: u(x, y) = 4x^3 − 18(x^2)y + 24x(y^2) − 120y Determine whether they are maxima, minima or saddle points. 2. Relevant equations To find stationary points use: E= (d^2u/dxy)^2 - [(d^2u/dx^2) * (d^2u/dy^2)] E>0 saddle E < 0 Maximum -> d^2u/dx^2 < 0 Minimum -> d^2u/dx^2 > 0 3. The attempt at a solution du/dx = 12x^2 - 36xy +24y^2 (1) du/dy = -18x^2 + 48xy-120 (2) Stationary points mean both du/dx and du/dy are equal to 0. Here I should find simultaneous solution of equations (1) and (2). This is where I get stuck and I am not sure how to find them. I have done the next part though: E= (-36x + 48y)^2 - (1152x^2 - 1728xy) But I need the stationary points to find the min/max/saddle points.