A. Find the gradient of f. Vƒ = 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 = Note: Your answer should be a number

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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Question

Suppose f(x,y)=xy, P=(2,1) and v=−3i−1j.

 

 

A. Find the gradient of f.
Vf =
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 =
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
Transcribed Image Text:A. Find the gradient of f. Vf = 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 = 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
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