MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Let f be continuous on [a,b] and differentiable on (a,b). The function has exactly one critical point c in (a,b), and f′′(c)>0. Which of the following statements must be true?
(a) f(c) is the absolute minimum value of f on [a,b].
(b) f(c) is a local maximum because f′′(c)>0.
(c) No conclusion about an absolute extremum can be drawn without evaluating f at a and b.
(d) f(c) cannot be an absolute extremum because c lies in the interior of the interval.