, Suppose f (x, y) = 4, P = (3,2) and v = 3i – 2j. - A. Find the gradient of f. (Vf)(x, y) : 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. (Vf) (P) = i+ j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. (Duf)(P) = Note: Your answer should be a number

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 22E: Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and...
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, Suppose f (x, y) = , P = (3,2) and v = 3i – 2j.
y'
A. Find the gradient of f.
(Vf)(x, y) =
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.
(Vf) (P) =
i+
j
Note: Your answers should be numbers
C. Find the directional derivative of f at P in the direction of v.
(Duf)(P) =
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 w in which the maximum rate of change occurs at P.
w =
i+
j
Note: Your answers should be numbers
Transcribed Image Text:, Suppose f (x, y) = , P = (3,2) and v = 3i – 2j. y' A. Find the gradient of f. (Vf)(x, y) = 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. (Vf) (P) = i+ j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. (Duf)(P) = 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 w in which the maximum rate of change occurs at P. w = i+ j Note: Your answers should be numbers
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