what conditions must be met to ensure that a function has an absolute maximum value and an absolute minimum…

what conditions must be met to ensure that a function has an absolute maximum value and an absolute minimum value on an interval? choose the correct answer below. a. the function must be continuous on a closed interval a,b. b. a critical point must occur on a closed interval on a,b. c. the function must be continuous for some subinterval on a,b. d. the function must be continuous on an open interval (a,b).

what conditions must be met to ensure that a function has an absolute maximum value and an absolute minimum value on an interval? choose the correct answer below. a. the function must be continuous on a closed interval a,b. b. a critical point must occur on a closed interval on a,b. c. the function must be continuous for some subinterval on a,b. d. the function must be continuous on an open interval (a,b).

Answer

Brief Explanations:

The Extreme - Value Theorem states that if a function is continuous on a closed interval [a, b], then the function has both an absolute maximum and an absolute minimum on that interval. A critical point is not a necessary condition for the existence of absolute extrema on a closed - interval. Continuity on a sub - interval is not sufficient, and continuity on an open interval does not guarantee absolute extrema.

Answer:

A. The function must be continuous on a closed interval [a,b]