Consider the function f(x, y, z) = xy+yz² + xz*. Find the gradient of f: • x+z? 2yz +3z²x Find the gradient of f at the point (3, -2, -1): -3 4 13 Find the rate of change of the function f at the point (3, -2,-1) in the direction u = (2,3, 2):

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the function f(x, y, z) = xy+yz² + xz*. Find the gradient of f:
(y+z3
· x+z?
2yz + 3z²x
Find the gradient of f at the point (3, -2, -1):
(-3
4
13
Find the rate of change of the function f at the point (3, -2,-1) in the direction u =
= (2, 3, 2):
Transcribed Image Text:Consider the function f(x, y, z) = xy+yz² + xz*. Find the gradient of f: (y+z3 · x+z? 2yz + 3z²x Find the gradient of f at the point (3, -2, -1): (-3 4 13 Find the rate of change of the function f at the point (3, -2,-1) in the direction u = = (2, 3, 2):
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