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?
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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