Transcribed Image Text: ) Suppose f (x, y) = ,

P = (-2,2) and v = -3i + lj.

A. Find the gradient of f.

Vf =

1/y

E i+ -xy^-2

j

Note: Your answers should be expressions of x and y; e.g. “3x – 4y”

B. Find the gradient of f at the point P.

(Vf)(P) =

1/2

i+ 1/2

j

Note: Your answers should be numbers

C. Find the directional derivative of f at P in the direction of v.

Duf =

Note: Your answer should be a number

D. Find the maximum rate of change of f at P.

Note: Your answer should be a number

E. Find the (unit) direction vector in which the maximum rate of change occurs at P.

u =

i+

j

Note: Your answers should be numbers