Let f (x, y, z) be a function such that : (i) the function f (x, y, z) decreases most rapidly at the point P(1, 2, 2) in the direction of the vector (8,-4, -1). (ii) the Minimum rate of change of f (x, y,z) at the point P is -18. Find the directional derivative of f (x,y,z) at the point P in the direction from the point P towards the point Q(-1,0, 3).

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...
icon
Related questions
Question
Let f (x, y, z) be a function such that :
(i) the function f (x, y, z) decreases most rapidly at the point P(1, 2, 2) in
the direction of the vector (8, -4, -1).
(ii) the Minimum rate of change of f (x, y,z) at the point P is -18.
Find the directional derivative of f (x, y,z) at the point P in the direction
from the point P towards the point Q(-1,0, 3).
Enter an integer or a fully reduced fraction such as -2, 7, -3/4, 41/7 etc.
No spaces please.
Transcribed Image Text:Let f (x, y, z) be a function such that : (i) the function f (x, y, z) decreases most rapidly at the point P(1, 2, 2) in the direction of the vector (8, -4, -1). (ii) the Minimum rate of change of f (x, y,z) at the point P is -18. Find the directional derivative of f (x, y,z) at the point P in the direction from the point P towards the point Q(-1,0, 3). Enter an integer or a fully reduced fraction such as -2, 7, -3/4, 41/7 etc. No spaces please.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning