Question

Suppose f (x,y) = x
y , P = (1,−4) and v = −2i+4j.
A. Find the gradient of f.
Ñf = 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.
(Ñf ) (P) = i+ j
Note: Your answers should be numbers
C. Find the directional derivative of f at P in the direction of
v.
Du f =
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
Answer(s) submitted:
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