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16. Suppose that over a region of space the electrical potential V is given by V(x, y, z) = 5x? – 3xy + xyz, find the following: a) Compute the rate of change of the potential at P (3, 4,5) in the direction of the vector v = (1,1,-1). b) In which direction does V change the most rapidly at P? c) Find the maximum rate of change at P.

16. Suppose that over a region of space the electrical potential V is given by V(x, y, z) = 5x? – 3xy + xyz, find the following: a) Compute the rate of change of the potential at P (3, 4,5) in the direction of the vector v = (1,1,-1). b) In which direction does V change the most rapidly at P? c) Find the maximum rate of change at P.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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16. Suppose that over a region of space the electrical potential V is given by V(x, y, z) = 5x? – 3xy + xyz, find the following: a) Compute the rate of change of the potential at P (3, 4,5) in the direction of the vector v = (1,1,-1). b) In which direction does V change the most rapidly at P? c) Find the maximum rate of change at P.
Transcribed Image Text:16. Suppose that over a region of space the electrical potential V is given by V(x, y, z) = 5x? – 3xy + xyz, find the following: a) Compute the rate of change of the potential at P (3, 4,5) in the direction of the vector v = (1,1,-1). b) In which direction does V change the most rapidly at P? c) Find the maximum rate of change at P.
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