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
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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.
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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