Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. f(x,y,z)=(x/y)-yz, Po(4,1,3) The direction in which the given function f(x,y,z) = (x/y) - yz increases most rapidly at Po(4,1,3) is u = (Type exact answers, using radicals as needed.) + + k. The direction in which the given function f(x,y,z) = (x/y) - yz decreases most rapidly at Po(4,1,3) is v=i+j+ k. (Type exact answers, using radicals as needed.) The derivative of the given function f(x,y,z) = (x/y) - yz in the direction in which the function increases most rapidly at Po(4,1,3) is Duf=. (Type an exact answer, using radicals as needed.) The derivative of the given function f(x,y,z) = (x/y) - yz in the direction in which the function decreases most rapidly at Po(4,1,3) is Dvf= (Type an exact answer, using radicals as needed.)
Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. f(x,y,z)=(x/y)-yz, Po(4,1,3) The direction in which the given function f(x,y,z) = (x/y) - yz increases most rapidly at Po(4,1,3) is u = (Type exact answers, using radicals as needed.) + + k. The direction in which the given function f(x,y,z) = (x/y) - yz decreases most rapidly at Po(4,1,3) is v=i+j+ k. (Type exact answers, using radicals as needed.) The derivative of the given function f(x,y,z) = (x/y) - yz in the direction in which the function increases most rapidly at Po(4,1,3) is Duf=. (Type an exact answer, using radicals as needed.) The derivative of the given function f(x,y,z) = (x/y) - yz in the direction in which the function decreases most rapidly at Po(4,1,3) is Dvf= (Type an exact answer, using radicals as needed.)
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:Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in
these directions.
f(x,y,z) = (x/y) - yz, Po(4,1,3)
...
The direction in which the given function f(x,y,z) = (x/y) — yz increases most rapidly at Po(4,1,3) is u =
(Type exact answers, using radicals as needed.)
The direction in which the given function f(x,y,z) = (x/y) — yz decreases most rapidly at P(4,1,3) is v=
(Type exact answers, using radicals as needed.)
Ji+j+ k.
Oj+ k.
li +
The derivative of the given function f(x,y,z) = (x/y) — yz in the direction in which the function increases most rapidly at Po(4,1,3) is
Duf=
(Type an exact answer, using radicals as needed.)
The derivative of the given function f(x,y,z) = (x/y) − yz in the direction in which the function decreases most rapidly at Po(4,1,3) is
Dyf=.
(Type an exact answer, using radicals as needed.)
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