Which of the following best distinguishes a local (relative) maximum from an absolute…
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Which of the following best distinguishes a local (relative) maximum from an absolute (global) maximum of a function f on a given interval?
(a) A local maximum must occur at an endpoint of the interval, while an absolute maximum cannot occur at an endpoint.
(b) An absolute maximum must always occur at a critical point, while a local maximum may occur at an endpoint.
(c) A local maximum is the greatest value of f within some open interval containing the point, whereas an absolute maximum is the greatest value of f on the entire interval.
(d) A local maximum is the greatest value of f on the entire interval, whereas an absolute maximum is the greatest value only within a small neighborhood of the point.