How do you determine the stationary points of the function f(x, y) = x² + xy + y² + 5x - 5y + 3?

To determine the stationary points of the function f(x, y) = x² + xy + y² + 5x - 5y + 3, calculate the partial derivatives ∂f/∂x and ∂f/∂y, set them equal to zero, and solve the resulting simultaneous equations.

First, compute the partial derivatives: ∂f/∂x = 2x + y + 5 and ∂f/∂y = x + 2y - 5. Next, set both partial derivatives to zero: 2x + y + 5 = 0 and x + 2y - 5 = 0. Solve these equations simultaneously to find the values of x and y that yield the stationary points.