Relative and Absolute Extrema

What do you notice about the graph of f(x) when g(x)=0?

Does the graph f(x) have relative extrema? If so, where are they? If not, how do you know?

Does the graph f(x) have absolute extrema? If so, where are they? If not, how do you know?

How would you know when the graph f(x) switches concavity?