Partial Derivative Analysis Question

[gathan77]

Homework Statement

Given a graph of f(x,y), how can you determine where the partial and second derivatives are positive, negative, or zero?

The attempt at a solution

The first partial derivative is fairly easy to picture so I'm more concerned about the second partial derivative. I'm having troubles imagining what this would look like and an explanation could come of use. Thanks in advance for the help.

 

[quasar987]

Take a loot at the notion of an "inflexion point" for a function of one variable. This should give you some intuition.