Note Extrema may occur at the endpoints a,b or at points in ( a;b).
Figure 5.13 shows the graph of a function f with domain [a;b]. Note that f attains its absolute minimum at x 2 which belongs to the open interval (a;b) and attains its absolute max-imum at b which is an endpoint. Also note that f has a relative maximum at x 1but it does not attains its absolute maximum there