1. Find the points on the ellipse 4x2 + y - 8 =0 where f(x, y) = xy has its extreme values. (Solve by hand, not using Mathematica. You'll use it in problem 3.) 2. Find the largest product the positive numbers x, y, and z can have if x + y + z = 16. (Solve by hand, not using Mathematica. You'll use it in problem 3.)