Question

Suppose ?(?,?)=??f(x,y)=xy, ?=(−4,−4)P=(−4,−4) and ?=3?+2?v=3i+2j. A. Find the gradient of f. ∇?=∇f=  ?+i+  ?j Note: Your answers should...

Suppose ?(?,?)=??f(x,y)=xy, ?=(−4,−4)P=(−4,−4) and ?=3?+2?v=3i+2j.

A. Find the gradient of f.
∇?=∇f=  ?+i+  ?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.
(∇?)(?)=(∇f)(P)=  ?+i+  ?j
Note: Your answers should be numbers

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

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

E. Find the (unit) direction vector in which the maximum rate of change occurs at P.
?=u=  ?+i+  ?

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