Quiz 2 - Take home Due : Wednesday Jan 27, 2016 Please hand in your quiz at the beginning of lecture on the due date 1. Let f (x, y) = xye−x−y . (i) Find all the critical points of f (x, y). (ii) Determine whether each point corresponds to a local maximum, local minimum, or saddle point. 2 2 2. Find the maximum and minimum values of the function f (x, y) = x + y on the boundary of the 2 2 region R = (x, y) : x + 4y ≤ 4 . 3. Use Lagrange multipliers to find the maximum and minimum values of xy + x + y on the curve C given by x2 y 2 = 16.