Key to Practice Midterm III

Problem 1

A.  True, alldirectional Derivatives at a critical point are zero.

B.  False, for example (1,-1) is not in the domain.

C.  True, f_u =  f_x x_u + f_y y_u  = (-1)(10) + (7)(5)

Problem 2 

The surface is an ellipsoid.

Problem 3

(1,2):  Saddle,    (1,-2):  Minimum,     (-1,2):  Maximum      (-1,-2): Saddle

Problem 4

A.  Does not Exist

B.  0

Problem 5

A.  -2xysin(xy²)

B.  -2ysin(xy²) - 2xy³cos(xy²)

Problem 6

.25%

Problem 7

0

Problem 8

3i-10j