Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 5x² - 5xy + xyz (a) Find the rate of change of the potential at P(4, 4, 7) 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?
Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 5x² - 5xy + xyz (a) Find the rate of change of the potential at P(4, 4, 7) 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?
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 17E: Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.
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