A gradient field (analysing a picture)

In summary, the conversation discusses the relationship between the gradient of a function and the change in function value as one moves from one level curve to another. The picture provided shows the gradient of the function and the question asks how the function value changes when starting at a specific point. The expert agrees that the function value increases slightly as one moves to the right due to the presence of a component in that direction in the gradient. However, the exact function is not given in the problem statement.
  • #1
Poetria
267
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?
 
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  • #2
Explain the relationship with the picture -- if any

What is the complete problem statement ?
 
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  • #3
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?
 
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  • #4
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.
 
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  • #5
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. :)
 

1. What is a gradient field?

A gradient field is a mathematical concept used to describe the rate and direction of change of a quantity over a given space. In the context of analyzing a picture, a gradient field can be used to represent the intensity or color changes in an image.

2. How is a gradient field calculated?

A gradient field is calculated by taking the partial derivatives of the quantity being measured with respect to each dimension in the given space. In the case of a picture, this would involve calculating the change in intensity or color along the x and y axes.

3. What does a gradient field tell us about a picture?

A gradient field can tell us about the overall changes in intensity or color in a picture, as well as the direction and magnitude of those changes. This information can be useful in analyzing the composition and visual impact of the picture.

4. How is a gradient field used in image processing?

In image processing, a gradient field can be used to enhance or manipulate certain features of a picture. For example, it can be used to sharpen edges or smooth out areas of a picture, depending on the desired effect.

5. Are there any limitations to using a gradient field to analyze a picture?

While a gradient field can provide valuable information about a picture, it is not always the most accurate or efficient method of analysis. Depending on the complexity of the picture and the desired level of detail, other techniques may be more suitable for analyzing the image.

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