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Now, for the
relative
minimums... Those are the bottoms of the valleys:
Relative mins are the
lowest points in their little
neighborhoods.
f
has a relative min of
-3
at x
=
-1.
f
has a relative min of
-1
at x
= 4.
YOUR TURN:
Find the relative extrema:
So, how many
relative mins and maxes 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
real zeros he might have 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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