Let f(x, y, z) = x² - cos(xy) + eYz. (a) At the point (3, 0, 1) compute the unit vector in the direction of maximum increase of the function f and compute the rate of increase in that direction. (b) Compute the directional derivative of the function f at the point (3,0,1) in the direction of the vector (-5, 12, 0).
Let f(x, y, z) = x² - cos(xy) + eYz. (a) At the point (3, 0, 1) compute the unit vector in the direction of maximum increase of the function f and compute the rate of increase in that direction. (b) Compute the directional derivative of the function f at the point (3,0,1) in the direction of the vector (-5, 12, 0).
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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![Let f(x, y, z) = x² - cos(xy) + eYz.
(a) At the point (3, 0, 1) compute the unit vector in the direction of maximum
increase of the function f and compute the rate of increase in that direction.
(b) Compute the directional derivative of the function f at the point (3,0,1) in
the direction of the vector (-5, 12, 0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F609191b6-0aff-477d-8910-61edd76acc39%2F8466d57b-3e6e-44c2-bbde-18823e4ae6e5%2Ffjw43b_processed.png&w=3840&q=75)
Transcribed Image Text:Let f(x, y, z) = x² - cos(xy) + eYz.
(a) At the point (3, 0, 1) compute the unit vector in the direction of maximum
increase of the function f and compute the rate of increase in that direction.
(b) Compute the directional derivative of the function f at the point (3,0,1) in
the direction of the vector (-5, 12, 0).
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