Suppose f (x, y) = , P = (-4, 4) and v = 2i + 3j. A. Find the gradient of f. (Vf)(x, y) i+ Note: Your answers should be expressions of x and y; e.g. "3x - 4y" = B. Find the gradient of f at the point P. (Vƒ) (P) = i+ 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 W = j E. Find the (unit) direction vector w in which the maximum rate of change occurs at P. i+ Note: Your answers should be numbers

Suppose f (x, y) = , P = (-4, 4) and v = 2i + 3j. A. Find the gradient of f. (Vf)(x, y) i+ Note: Your answers should be expressions of x and y; e.g. "3x - 4y" = B. Find the gradient of f at the point P. (Vƒ) (P) = i+ 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 W = j E. Find the (unit) direction vector w in which the maximum rate of change occurs at P. i+ Note: Your answers should be numbers

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 21E

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