Suppose a function f is continuous on [a,b] and differentiable on (a,b). It has exactly one critical number c in (a,b), and f′′(c)>0. Which of the following MUST be true?
a) f attains its absolute maximum at x=c on the interval [a,b].
b) f attains its absolute minimum at x=c on the interval [a,b].
c) f attains both its absolute minimum and its absolute maximum at x=c on [a,b].
d) f attains its absolute minimum at one of the endpoints x=a or x=b of the interval [a,b].