Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 2x2 - 5xy + xyz (a) Find the rate of change of the potential at P(5, 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) = 2x2 - 5xy + xyz (a) Find the rate of change of the potential at P(5, 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?
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.3: Vectors In The Plane
Problem 11ECP
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