(3) Let f(x, y) = y

2

e

xy + y

2

. Find fyx, and fxy.

(4) Find the directional derivative of f(x, y) = xy at P(1, 4) in the direction a =

3i 3j.

(5) Use a total differential to approximate the change in the values of f(x, y) = ln(

1 + xy)

from P(0, 2) to Q(0.09, 1.98). Compare your estimate with the actual change in

f. Find a local linear approximation of f at (0, 2).

(6) Find absolute extrema of f(x, y) = xy 4x on R where R is the triangular region

with vertices (0, 0), (4, 4) and (4, 4).