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Consider the function f(x, y, z) = xy + y² +². (a) What is the gradient grad f of f, and what is its value at the point (2,1,1)? (b) What is the rate of change of f at the point (2,1,1) in the direction of the unit vector = 1+4? (e) What is the maximum rate of change of f at the point (2,1,1), and in what direction does this maximum value occur?

Consider the function f(x, y, z) = xy + y² +². (a) What is the gradient grad f of f, and what is its value at the point (2,1,1)? (b) What is the rate of change of f at the point (2,1,1) in the direction of the unit vector = 1+4? (e) What is the maximum rate of change of f at the point (2,1,1), and in what direction does this maximum value occur?

Advanced Engineering Mathematics
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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Consider the function f(r, y, z) = ry +y? + 22. (a) What is the gradient grad f of f, and what is its value at the point (2, 1, 1)? (b) What is the rate of change of f at the point (2, 1,1) in the direction of the unit vector în =i+j? (c) What is the maximum rate of change of f at the point (2,1,1), and in what direction does this maximum value occur?
Transcribed Image Text:Consider the function f(r, y, z) = ry +y? + 22. (a) What is the gradient grad f of f, and what is its value at the point (2, 1, 1)? (b) What is the rate of change of f at the point (2, 1,1) in the direction of the unit vector în =i+j? (c) What is the maximum rate of change of f at the point (2,1,1), and in what direction does this maximum value occur?
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