Local and Global Extrema - Expii
A local minimum (resp. maximum) is a lowest (resp. highest) value attained by a function on some interval (not necessarily lowest or highest on the whole domain or interval). A global minimum (resp. maximum) is the lowest (resp. highest) value attained by a function on the whole domain or interval. All global extrema (global maxima or minima) are local extrema (local maxima or minima), but not vice versa. All of these concepts can be visualized nicely on the graph y=f(x), in terms of highest and lowest points.