Finding Rel. Max, Min, and Saddle Points on Levelset

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Points A-E on the level sets represent different types of critical points for the function depicted in the diagram. Point B is identified as a relative maximum, while the classifications for points A, C, D, and E remain uncertain. Participants in the discussion express confusion over these classifications and seek clarification on how to determine the nature of each point based on the level sets. The conversation highlights the challenge of visualizing and interpreting level sets in relation to critical points. Overall, the discussion emphasizes the need for a clearer understanding of relative minima, maxima, and saddle points in the context of level sets.
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Homework Statement



The diagram above represents a collection of level sets for a certain function, where the outer-most level is at the lowest height.

What are points A-E? relative min, relative max, saddle point, or not a critical point


The Attempt at a Solution



I have tried multiple times to get this question right, but I keep failing.

I know that point B is a relative Maximum.
What would C, D , and A be?

Thanks for your help!
 

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Does Anyone have any Ideas? I don't think its that difficult of a question for some, but its just a little bit confusing.
 

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