How Do You Determine Lines of Maxima and Minima Based on Gradient?

[385sk117]

Homework Statement

Please look at the attached picture
In that I had to draw the line of maxima and minima

Homework Equations

line of maxima has greatest gradient
line of minima has smallest gradient

The Attempt at a Solution

which line should be the maxima? the line with the greatest gradient right?
and as the gradient of the lines are negative here, the most flat line will be the line of maxima? or i have to look at the absolute values of gradient?

 

[Nate810]

The line of maxima should be the one with the greatest absolute value of gradient. In this case, the line with the greatest absolute value of gradient is the bottom line. Therefore, the bottom line should be the line of maxima.

 

[nlightner]

I would like to clarify that the concept of "line of maxima and minima" may not be well-defined in the context of this image. It is important to have a clear understanding of the variables and their relationships in order to accurately identify lines of maximum and minimum values. In this case, without knowing the specific data or function being represented, it is difficult to determine which lines would correspond to maxima or minima. Additionally, the concept of "gradient" may not be applicable to this situation unless we have a clear definition of what is being measured and how it is changing. It is important to approach scientific problems with precision and clarity to avoid misinterpretations and inaccuracies.