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Maximums and Minimums: Finding Relative Extrema

Look back at the graph...

the relative maximums of the graph are 2 at x = -3 and 1 at x = 2 ... the guys in the interval ( 4 , infinity ) keep going and beat out our relative maximums, but we don't care!

(Relative extrema (maxs & 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.