1. Determine whether the statement is sometimes, always, or never true
Determine whether the statement is sometimes, always, or never true. The graph of a polynomial of degree three will intersect the x-axis three times.
Draw picture(s) to illustrate the choice you made.

2. 4-5 Analyzing Graphs of Polynomials
Graph polynomial functions and locate their zeros
Find relative maxima or minima of polynomial functions

4. The absolute max is the highest y-value.
I'll make this really quick and simple:
The absolute max is the highest y-value.  
The absolute min is the lowest y-value.  
Check it out:
f has an absolute max of 2 at x = 2. (This is also a relative max!)
f has an absolute min of -2 at x = -3. (This cannot be a relative min, since it doesn't have points on BOTH sides to compare it to.)
Endpoints CAN be absolute extrema!
Endpoints cannot be relative extrema!

5. Check out this graph:
The tops of the mountains are relative maximums because they are the highest points in their little neighborhoods (relative to the points right around them):

6. Suppose you're in a roomful of people (like your classroom). 
Find the tallest person there.  (It's usually a guy.)
He is the relative max of that room.  Specifically, he's the 
tallest relative to the people around him.   But, what if you took
that guy to an NBA convention? 
There'd be lots of guys who beat him.

7. (Relative extrema (maxs and mins) are sometimes called local extrema.)
Other than just pointing these things out on the graph, we have a very specific way to write them out.
Officially, for this graph, we'd say:
f has a relative max of 2 at x = -3.
f has a relative max of 1 at x = 2.
The max is, actually, the height...  the x guy is where the max occurs.
So, saying that the max is (-3, 2) would be unclear and not really correct.

8. f has a relative min of -1 at x = 4.
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.

9. Remember, we use how many real zeros he might have to guide us.
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.                   
a plain  

10. A polynomial of degree n can have, at most, n - 1 relative extrema.
Hmm...  It looks like an    guy can have, at most, 
3 relative extrema.
What about ?
   guy can have, at most, 4 relative extrema.
See a pattern?
A polynomial of degree n can have, at most, n - 1 relative extrema.