Finding critical points from level curves

[triden]

Homework Statement

I was given the following level curve (image is attached). I need to find the critical points and classify them (local max, min, saddle).

The Attempt at a Solution

I can find the points easily enough. Saddle at (-1,0), and then locals at each of the three circles. However, I cannot figure out if they are local max or mins. How can I tell from the surface if it is a max or a min? To me it looks as though it could go either way.

Thanks,

Chris

 

[HallsofIvy]

Look at the z-values of the level curves close to the points. Are they increasing or decreasing as you move toward the critical point?

 

[triden]

Ah got it...I knew it was simple, just didn't catch that those were the Z values. Thanks