Which of the following statements most accurately states the Extreme Value Theorem (EVT)?
MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
Which of the following statements most accurately states the Extreme Value Theorem (EVT)?
(a) If f is continuous on (a,b), then f attains both an absolute maximum value and an absolute minimum value on (a,b).
(b) If f is continuous on [a,b], then f attains both a local maximum value and a local minimum value on (a,b).
(c) If f is continuous on [a,b], then f attains both an absolute maximum value and an absolute minimum value on [a,b].
(d) If f is continuous on [a,b] and differentiable on (a,b), then f attains exactly one absolute maximum value and exactly one absolute minimum value on [a,b].