Question

(1 point) Suppose f (x, y) = x/y, P = (-1, 2) and v = -4i + 4j. 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. 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

          (1 point) Suppose f (x, y) = x/y, P = (-1, 2) and v = -4i + 4j.

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.
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

(1 point) Suppose f (x, y) = x/y, P = (-1, 2) and v = -4i + 4j.

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.
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

Added by Craig E.

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