(iii) Find the gradient of the function g(x, y, z) = (4√z - x)y² at the point (4, 1, 4) and give the coordinates of the unit vector u in the direction of the vector (2, 1, 2). Hence, calculate the directional derivative Dug(4, 1,4). Also give the direction of maximum increase of the function g at any general point and at the point (4, 1, 4) as unit vector.
(iii) Find the gradient of the function g(x, y, z) = (4√z - x)y² at the point (4, 1, 4) and give the coordinates of the unit vector u in the direction of the vector (2, 1, 2). Hence, calculate the directional derivative Dug(4, 1,4). Also give the direction of maximum increase of the function g at any general point and at the point (4, 1, 4) as unit vector.
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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Transcribed Image Text:(iii) Find the gradient of the function g(x, y, z) = (4√z - x)y² at the point (4, 1, 4) and give the
coordinates of the unit vector u in the direction of the vector (2, 1, 2). Hence, calculate the
directional derivative Dug (4, 1, 4). Also give the direction of maximum increase of the function g
at any general point and at the point (4, 1, 4) as unit vector.
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