Consider the function f(x, y, z) = xy + yz²+xz³. Find the gradient of f: 000 Find the gradient of f at the point (5, —1, −5). 000 Find the rate of change of the function f at the point (5, −1, −5) in the direction u = (-3/√/19, 1/√/19, -3/√19).

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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Consider the function f(x, y, z) = xy + yz² + xz³.
Find the gradient of f:
000
Find the gradient of f at the point (5, —1, −5).
000
Find the rate of change of the function f at the point (5, −1, −5) in the direction
u = (-3/√19, 1/√19, -3/√19).
Transcribed Image Text:Consider the function f(x, y, z) = xy + yz² + xz³. Find the gradient of f: 000 Find the gradient of f at the point (5, —1, −5). 000 Find the rate of change of the function f at the point (5, −1, −5) in the direction u = (-3/√19, 1/√19, -3/√19).
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