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).
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 ________.
Related questions
Question
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F937c5b24-3686-40bc-8921-1d1fed2f5241%2Fe95aa381-a421-4fc4-8409-abbc6db72704%2F0nyb46u_processed.png&w=3840&q=75)
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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