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Suppose f (x, y) = , P = (-2, -1) and v = 2i - 4j. A. Find the gradient of f. (Vƒ)(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

Suppose f (x, y) = , P = (-2, -1) and v = 2i - 4j. A. Find the gradient of f. (Vƒ)(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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose f (x, y) = , P = (-2, -1) and v = 2i - 4j. A. Find the gradient of f. (Vƒ)(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 = (-2, -1) and v = 2i - 4j. A. Find the gradient of f. (Vƒ)(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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