|
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,
at most, n - 1
relative extrema. |
|
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