When finding the absolute maximum or minimum of a continuous function on a closed interval
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
When finding the absolute maximum or minimum of a continuous function on a closed interval [a,b], why must the function be evaluated at the endpoints a and b in addition to its critical points?
(a) Because the derivative is always zero at the endpoints
(b) Because the endpoints may give extreme values even when the derivative is non–zero there
(c) Because Rolle’s Theorem requires comparing the function values at the endpoints
(d) Because endpoints are boundary points that automatically maximize or minimize the function