Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z)= 3x2 - 4xy + xyz (a) Find the rate of change of the potential at P(5, 6, 6) in the direction of the vector v = i + j - k. (b) In which direction does V change most rapidly at P? (c) What is the maximum rate change at P?

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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Suppose that over a certain region of space the electrical potential V is given by the following equation.
V(x, y, z) = 3x² - 4xy + xyz
(a) Find the rate change of the potential at P(5, 6, 6) in the direction of the vector v=i+j-k.
(b) In which direction does V change most rapidly at P?
(c) What is the maximum rate of change at P?
Transcribed Image Text:Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 3x² - 4xy + xyz (a) Find the rate change of the potential at P(5, 6, 6) in the direction of the vector v=i+j-k. (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P?
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