(a) Use software that plots implicitly defined curves to estimate the minimum and maximum values of f(x, y) = x³ + y³ + 3xy subject to the constraint (x − 3)² + (y − 3)² = 9 by graphical methods.

(b) Solve the problem in part (a) with the aid of Lagrange multipliers. You will need to solve the equations numerically. Compare your answers with those in part (a).