A gradient field (analysing a picture)

[Poetria]

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)

I think it is increasing as you move from one level curve to the other with bigger value. Am I right?

 

[BvU]

Explain the relationship with the picture -- if any

What is the complete problem statement ?

 

[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?

 

[FactChecker]

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.

 

[Poetria]

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. :)