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.