A gradient field (analysing a picture)

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The discussion centers on analyzing a gradient field depicted in a provided picture, focusing on how the function value changes as one moves along the gradient. It is confirmed that moving slightly to the right from the point (1, -1) results in an increase in the function value due to the gradient's directional component. Participants agree on the relationship between the gradient and the function's behavior in the specified region. The conversation emphasizes understanding the gradient's influence on function values without needing the explicit function itself. Overall, the analysis highlights the importance of gradient direction in determining changes in function values.
Poetria
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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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Explain the relationship with the picture -- if any

What is the complete problem statement ?
 
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?
 
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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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. :)
 

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