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) = zy + x + y subject to ray' = 4. 2. Use the second derivative test to classify the critical points of the function f (x, y) = rye (2+v) . 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. 4. Problem 10 from section 14.8 and problem 46 from section 14.7. 5. Explain, in your own words, the meaning of fry by considering the curve that is traced out when considering a as a fixed constant