So, how many relative mins and maxs does the typical polynomial critter have?
Don't know? When in doubt, draw pictures!
Let's draw some possible shapes of
Remember, we use how many times he can cross (his degree) to guide us.

Hmm... It looks like an guy can have, at most, 3 relative extrema.
What about  ?  
(I'll let you do the drawing.) 
It looks like an guy can have, at most, 4 relative extrema.
I smell a theorem brewing! (Either that or it's because I didn't shower this morning.)
A
polynomial of degree
n can
have, 