MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Let h be a continuous function on the interval (−2,5]. Which of the following best justifies whether h is guaranteed to attain an absolute minimum on that interval?
(a) Yes. The function is continuous on a bounded interval, so by the EVT it must attain an absolute minimum.
(b) No. The interval is not closed at x=−2, so the hypotheses of the EVT are not satisfied.
(c) No. The EVT requires differentiability as well as continuity, which h may not possess.
(d) Yes. Since h is continuous on (−2,5], it must attain an absolute minimum somewhere on the interval.