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 (z, y) = aly subject to 3x + 2y = 12. (b) Find the maximum and minimum (if they exist) of f (r, y) = zy + x + y subject to ry? = 4. 2. Use the second derivative test to classify the critical points of the function f (x, y) = rye-(2+y) . 3. Find the absolute max and min of the function f (x,y) = 2x2 - 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