In what direction ữ is f(x, y, z) increasing most rapidly at the point (1, 1, 0)? Give your answer as a unit vector ū. What is the directional derivative of f
In what direction ữ is f(x, y, z) increasing most rapidly at the point (1, 1, 0)? Give your answer as a unit vector ū. What is the directional derivative of f
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...
Related questions
Question
Can you explain how we got the <2i,3j,6k> in step 1 of the solution
![Solution.
• We have
2y
+1
(2 + y? – 1
2x
Vf(x,y, 2) = ( ,
i+
a? + у2 — 1
+ 6k.
Thus
Vf(1,1,0) = 27 + 33+ 6k.
The function f is most rapidly increasing in the direction
Vf
1
(27 + 35+ 6k).
|Vf|
7
• The directional derivative of f in the direction u is
df
dt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29aa648b-ab0c-4aa6-8222-785298870200%2F309f13aa-d4b8-4c15-97d1-c5158ff7c9ad%2F9jyzrtm_processed.png&w=3840&q=75)
Transcribed Image Text:Solution.
• We have
2y
+1
(2 + y? – 1
2x
Vf(x,y, 2) = ( ,
i+
a? + у2 — 1
+ 6k.
Thus
Vf(1,1,0) = 27 + 33+ 6k.
The function f is most rapidly increasing in the direction
Vf
1
(27 + 35+ 6k).
|Vf|
7
• The directional derivative of f in the direction u is
df
dt
![8. Let
f (x, y, z) = ln (x² + y? – 1) + y + 6z.
In what direction i is f(x, y, z) increasing most rapidly at the point (1, 1,
0)?
Give your answer as a unit vector ū. What is the directional derivative of f
in the direction u?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29aa648b-ab0c-4aa6-8222-785298870200%2F309f13aa-d4b8-4c15-97d1-c5158ff7c9ad%2F2ctozc8_processed.png&w=3840&q=75)
Transcribed Image Text:8. Let
f (x, y, z) = ln (x² + y? – 1) + y + 6z.
In what direction i is f(x, y, z) increasing most rapidly at the point (1, 1,
0)?
Give your answer as a unit vector ū. What is the directional derivative of f
in the direction u?
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