Consider the function: z = f(x, y) = x x y + xy. i. Find the domain and range of f. ii. Find the gradient vector of f(x, y). Call it V. iii. Solve V0 to find all of the critical points (x, y) of f(x, y). iv. Define the second order conditions and use them to classify each critical point as a maximum, minimum or a saddle point.