Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 3x² – 5xy + xyz (a) Find the rate of change of the potential at P(6, 2, 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) = 3x² – 5xy + xyz (a) Find the rate of change of the potential at P(6, 2, 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?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter20: Electric Potential And Capacitance

Section: Chapter Questions

Problem 23P

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