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Find a unit vector in the direction in which f(x, y, z) = 2x³z² + 2y³z + 250z − 2 increases most rapidly at P(5, 5, -1), and find the rate of change of f at P in that direction.

Find a unit vector in the direction in which f(x, y, z) = 2x³z² + 2y³z + 250z − 2 increases most rapidly at P(5, 5, -1), and find the rate of change of f at P in that direction.

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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Find a unit vector in the direction in which f(x, y, z) = 2x³z² + 2y³z + 250z − 2 increases most rapidly at - P(5,5, -1), and find the rate of change of f at P in that direction. NOTE: Enter the exact answers. u= ||Vf (5, 5, -1) || =
Transcribed Image Text:Find a unit vector in the direction in which f(x, y, z) = 2x³z² + 2y³z + 250z − 2 increases most rapidly at - P(5,5, -1), and find the rate of change of f at P in that direction. NOTE: Enter the exact answers. u= ||Vf (5, 5, -1) || =
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