Suppose that over a certain region of space the electrical potential V is given by V (x,y,z) = 3.x² – 2xy + 5xyz i. In what direction does V change most rapidly at the point P (3,4,5)? ii. What is the maximum rate of change of V at P (3,4,5)? iii. Find the rate of change of the potential at P (3,4,5) in the direction of the vector v =i-j+k
Suppose that over a certain region of space the electrical potential V is given by V (x,y,z) = 3.x² – 2xy + 5xyz i. In what direction does V change most rapidly at the point P (3,4,5)? ii. What is the maximum rate of change of V at P (3,4,5)? iii. Find the rate of change of the potential at P (3,4,5) in the direction of the vector v =i-j+k
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Suppose that over a certain region of space the electrical potential V is given by
V (x,y,z) = 3.x2 – 2.xy + 5xyz
-
i. In what direction does V change most rapidly at the point P (3,4,5)?
ii. What is the maximum rate of change of V at P (3,4,5)?
iii. Find the rate of change of the potential at P (3,4,5) in the direction of the vector v =i-j+k.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F789a23d3-cc6c-468c-ad55-03ca632fac8f%2F04da1af7-e92d-49de-82fe-c55067a575dc%2Fgyhk7lr_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that over a certain region of space the electrical potential V is given by
V (x,y,z) = 3.x2 – 2.xy + 5xyz
-
i. In what direction does V change most rapidly at the point P (3,4,5)?
ii. What is the maximum rate of change of V at P (3,4,5)?
iii. Find the rate of change of the potential at P (3,4,5) in the direction of the vector v =i-j+k.
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