Critical points are where

or where

is undefined. Let's look at

and

when

, so that is a critical point. So now let's take a value to the "left" of 0 (any negative number). Let's just pick

for simplicity.

, which means that when

,

is decrease (you can look at the graph to verify[/tex]. If

, that means

is decreasing. If we pick 1, we'll see the opposite.

Remember: If

is negative on some interval, then

is decreasing on that interval, and the opposite is true. And if

, or if

is undefined at some point, then that point is a critical point, and could be a local extreme.

A simple sign diagram for

A diagram that may be helpful: