Name :
Score:
Math 148 Quiz 9: §10.5–10.6
Directions: Answer each question completely.
credit, and circle your final answer.
1. Let z =
Show all work to receive full
p
dz
x2 + y 2 where x = t and y = sin t. Find
when t = π.
dt
2. Find the local extrema and saddle points of f (x, y) = e−(x
1
2 +y 2 )
.
3. Let f (x, y) = 2xy 3 − 3x2 y.
(a) Find the gradient of f .
(b) Find the directional derivative of f at the point (2, 1) in the direction of the vector
~v = h1, 1i.
(c) In which direction does f increase most rapidly at (2, 1)? What is the maximum
rate of change?
2