Assuming that the necessary derivatives of f(x,y,z) are defined, how are Dif, Dif, and Df related to f, fy, and f,? Give reasons for your answer. Choose the correct answer below. O A. D,f, D,f, and Df are equal to fy, fy, and f, respectively, because when u i, the directional derivative at Po is f, evaluated at that point, when u j, the directional derivative at Po is f, evaluated at that point, when u k, the directional derivative at Po is f, evaluated at that point 0 X O B. D,f, D,f, and Df are not related to fy, fv, and f,. O C. D,f, D,f, and Df represent the rate of change in the same direction as fy, f, and f, respectively, because directional vectors and gradient vectors have the same direction.
Assuming that the necessary derivatives of f(x,y,z) are defined, how are Dif, Dif, and Df related to f, fy, and f,? Give reasons for your answer. Choose the correct answer below. O A. D,f, D,f, and Df are equal to fy, fy, and f, respectively, because when u i, the directional derivative at Po is f, evaluated at that point, when u j, the directional derivative at Po is f, evaluated at that point, when u k, the directional derivative at Po is f, evaluated at that point 0 X O B. D,f, D,f, and Df are not related to fy, fv, and f,. O C. D,f, D,f, and Df represent the rate of change in the same direction as fy, f, and f, respectively, because directional vectors and gradient vectors have the same direction.
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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How are the directional derivative and partial derivative related (more information in the image)
Transcribed Image Text:Assuming that the necessary derivatives of f(x,y,z) are defined, how are Dif, Dif, and Df related to f, fy, and f,? Give reasons for your answer.
Choose the correct answer below.
O A. D,f, D,f, and Df are equal to fy, fy, and f, respectively, because when u i, the directional derivative at Po is f, evaluated at that point, when u j, the directional derivative at Po is f, evaluated at that point,
when u k, the directional derivative at Po is f, evaluated at that point
0
X
O B. D,f, D,f, and Df are not related to fy, fv, and f,.
O C. D,f, D,f, and Df represent the rate of change in the same direction as fy, f, and f, respectively, because directional vectors and gradient vectors have the same direction.
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