MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A function h is continuous on [0,5] and differentiable on (0,5). The function has exactly one critical point at x=2, but h′′(2)=0. Which statement is most accurate?
(a) x=2 must be a point of inflection because h′′(2)=0.
(b) No conclusion about an absolute extremum at x=2 can be drawn without additional information.
(c) x=2 must be the absolute maximum of h on [0,5] because it is the only critical point.
(d) Because h′′(2)=0, x=2 cannot be an extremum; the absolute extrema must occur at the endpoints x=0 or x=5.