A gradient field (analysing a picture)

Click For Summary

Homework Help Overview

The discussion revolves around analyzing a gradient field based on a provided picture and understanding how the function value changes as one moves within that field. The context involves concepts from vector calculus, specifically relating to gradient functions and level curves.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to interpret the relationship between the gradient field and the function values as one moves through the field. Questions about the complete problem statement and the implications of the gradient's direction are raised.

Discussion Status

Some participants have expressed agreement on the interpretation of the gradient's effect on the function value, noting that moving in the direction of the gradient results in an increase in the function value. However, the discussion remains open with questions about the initial problem statement and the specific function being analyzed.

Contextual Notes

There is a mention of a missing function definition, which may limit the depth of analysis. The discussion also references a specific point in the gradient field, indicating a focus on local behavior rather than a global understanding.

Poetria
Messages
267
Reaction score
42
Homework Statement
The gradient of the function f.
R - the region inside and on the boundary of the circle.
You start at the point (1,-1) and move slightly to the right. How does the value of f change?
Relevant Equations
The function has its maximum at the point (0, -2)
Gradient-field.jpg
I think it is increasing as you move from one level curve to the other with bigger value. Am I right?
 
Physics news on Phys.org
Explain the relationship with the picture -- if any

What is the complete problem statement ?
 
Reply
  • Like
Likes   Reactions: Poetria
Well, you have the picture I have posted. And you should answer the question I have posted. The function isn't given.

"Here is a picture of the gradient of a function f . Let R denote the region inside and on the boundary of the circle."
"If you start at the point (1, -1) and move slightly to the right, how does the value of f change?
 
Reply
  • Like
Likes   Reactions: BvU
I agree with your answer. The gradient has a component in your direction going to the right, so the function value is increasing slightly as you move right.
 
Reply
  • Like
Likes   Reactions: BvU and Poetria
FactChecker said:
I agree with your answer. The gradient has a component in your direction going to the right, so the function value is increasing slightly as you move right.
Great. :) Thank you very much. :)
 

Similar threads

Lagrange multipliers understanding
  • · Replies 8 ·
Replies
8
Views
2K
Why can some gradient fields not be simply connected?
  • · Replies 6 ·
Replies
6
Views
2K
Surface integrals of vector fields, normal - does scaling matter?
  • · Replies 7 ·
Replies
7
Views
2K
What is the Maximum Rate of Change in Scalar Fields?
  • · Replies 4 ·
Replies
4
Views
2K
What is the one-dimensional counterpart to the Green-Gauss theorem?
  • · Replies 28 ·
Replies
28
Views
2K
Undergrad How can concentration gradient field come into existence immediately?
  • · Replies 1 ·
Replies
1
Views
3K
Finding the gradient to the curve using differentiation
  • · Replies 2 ·
Replies
2
Views
1K
Two cards are drawn from a deck without replacement
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad What's the physical meaning of Curl of Curl of a Vector Field?
  • · Replies 5 ·
Replies
5
Views
2K
Unit vector perpendicular to the level curve at point
  • · Replies 4 ·
Replies
4
Views
3K