Math 208 (Lutz) - Quiz #5, 9/27/13
Name:
Directions: This quiz has 3 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. (6 points) For the function g(x, y) = sin(xy), find the maximum rate of increase of g at (1, 0) and the
direction in which this increase occurs.
2. (7 points) Consider a function f given by f (x, y, z) = x2 yz − xyz 3 . Find the directional derivative of
f at (2, −1, 1) in the direction of !u = 0!i + 45!j − 35 !k.
3. (7 points) Suppose z = f (x, y) = cos(x + 4y), where x = 5t4 and y = 1/t. Let z = g(t). Compute
g ! (t) directly and with the chain rule. Show that the two methods yield the same solution.