Consider the function f(x, y) = xy and the ellipse 422 + y = 8. Here we find the maximum and minimum values of on the ellipse using three approaches. (a) Plot (and label) several level curves of f. Also plot the ellipse. Add to the plot the points where you estimate that the maximum and minimum values of f restricted to the ellipse are attained. (b) Find the maximum and minimum values of f on the ellipse using substitution, and state where they are attained. (c) Find the maximum and minimum values of f on the ellipse, and where they are attained, using Lagrange multipliers.