Suppose f (x, y) = 1æ² + 2ry– 3y, P = (1,-3), and u = (, 8). %3D 20 20 A. Compute the gradient of f. Vf% = Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Evaluate the gradient at the point P. (Vf) (1,-3) = Note: Your answers should be numbers C. Compute the directional derivative of f at P in the direction u . (Duf) (P) = Note: Your answer should be a number

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 33E
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Question
20 20
Suppose f (x, y) = 1a? + 2ry – 3y, P = (1, -3), and u = (, 10).
A. Compute the gradient of f.
i+
j
Vf =
"3x - 4y"
Note: Your answers should be expressions of x and
y; e.g.
B. Evaluate the gradient at the point P.
i+
(Vf) (1,-3) =
Note: Your answers should be numbers
C. Compute the directional derivative of f at P in the direction u .
(Duf)(P)=
Note: Your answer should be a number
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Transcribed Image Text:20 20 Suppose f (x, y) = 1a? + 2ry – 3y, P = (1, -3), and u = (, 10). A. Compute the gradient of f. i+ j Vf = "3x - 4y" Note: Your answers should be expressions of x and y; e.g. B. Evaluate the gradient at the point P. i+ (Vf) (1,-3) = Note: Your answers should be numbers C. Compute the directional derivative of f at P in the direction u . (Duf)(P)= Note: Your answer should be a number Previous rch Th 68°F **- Home End Insert F8 F9 F10 F12 %23 & * 3 4 7 8 E R O P { F J K с V B N M V
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