Consider the function f(r, y, z) = ry + y² + z². (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?
Consider the function f(r, y, z) = ry + y² + z². (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?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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Q4
Transcribed Image Text:Consider the function f(r, y, z) = xy+ y² + z².
(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 n=÷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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