What are math extremes?

In short, math extreme is the highest (or lowest) value of a math function on an interval (a,b). For example, function y=x2 has minimum (extreme) for x=0 on interval (minus infinity, plus infinity). Similarly, function y=-x2 has maximum (extreme) for x=0 on the same interval. Some functions have multiple extremes, which are called local extremes, but this is enough for basic understanding of the principle.