Math 208 (Lutz) - Quiz #5, 2/21/14
Name:
Directions: This quiz has 2 questions, for a total of 20 points. Solve each problem carefully. You must
show ALL of your work in order to earn full credit.
1. Consider the function f (x, y) = (cos x)(cos y).
(a) (3 points) Verify that f has a critical point at (0, 0).
(b) (5 points) Use the discriminant to classify the critical point (0, 0) as either a local maximum,
local minimum, or saddle point.
2. (12 points) Use Lagrange multipliers to find the maximum and minimum values of f (x, y) = x + 3y + 2
subject to the constraint x2 + y 2 ≤ 5.
(Note: You do not need to use the discriminant to verify that the points you find are local extrema.)