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Maximums and Minimums: Finding Relative Extrema

Another huge thing in Calculus is finding relative extrema.

Check out this graph:

a graph of a polynomial with relative extrema at ( -3 , 2 ) , ( -1 , -3 ) , ( 2 , 1 ) , ( 4 , -1 )

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):

the relative maximums are at the highest points on the "mountains" of the graph

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.