Show all work to receive any credit. Correct answers without supporting work will receive NO credit! 1. Use Lagrange multipliers for each of the following : (a) Find the maximum value of f (x, y) = aly subject to 3x + 2y = 12. (b) Find the maximum and minimum (if they exist) of f (z, y) = ry + x + y subject to x y' = 4. 2. Use the second derivative test to classify the critical points of the function f(x, y) = rye-(2+) . 3. Find the absolute max and min of the function f (x, y) = 212 - 4x + 3y + 2 over the circle (x - 1) +y's 1. 5. Explain, in your own words, the meaning of fyy by considering the curve that is traced out when considering a as a fixed constant