4. Let f(x, y, z) = = xy + exp (z)y + z. a. Find Vf. b. Let u = (-1, -2, 1) and a = (1, 2, log 7). Using the limit definition of the directional derivative, find Du[f] (a). c. Now use the equation Du[f] = (Vf) u to find the same quantity. d. At a, find the maximum rate of change of f, and a unit vector pointing in the direction of maximal
4. Let f(x, y, z) = = xy + exp (z)y + z. a. Find Vf. b. Let u = (-1, -2, 1) and a = (1, 2, log 7). Using the limit definition of the directional derivative, find Du[f] (a). c. Now use the equation Du[f] = (Vf) u to find the same quantity. d. At a, find the maximum rate of change of f, and a unit vector pointing in the direction of maximal
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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.
c. Now use the equation Du[f] = (Vƒ) · u to find the same quantity.
d. At a, find the maximum rate of change of f, and a unit vector pointing in the direction of maximal
change.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69cce4ac-4bf6-4e6b-8636-bf160e045b58%2F8381abb1-a6ff-4f95-aa45-13861198f705%2Fx682yu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Let
a. Find Vf.
b. Let u
=
: (-1, -2, 1) and a
=
f(x, y, z) = xy + exp (z)y + z.
(1, 2, log 7). Using the limit definition of the directional derivative,
find Du[ƒ](a).
c. Now use the equation Du[f] = (Vƒ) · u to find the same quantity.
d. At a, find the maximum rate of change of f, and a unit vector pointing in the direction of maximal
change.
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