Final answer:
The absolute maximum and minimum values of a cubic function on an interval can occur at critical points or the endpoints. The exact determination cannot be made without the specifics of the cubic function, making option (d) that indicates we need the specific function (f(x)) the most accurate and universally correct option.
Step-by-step explanation:
To estimate the absolute maximum and minimum values of a cubic function (f(x)) on a given interval using a graphing utility, one would look for the highest and lowest points on the graph within that interval. Calculus methods involve finding the first derivative f'(x) to determine critical points, where the derivative is zero or undefined, and then testing these points alongside the endpoints of the interval to determine absolute extrema. If the function is continuous on a closed interval, as a cubic function generally is, the absolute maximum and minimum can occur at either the critical points or the endpoints. Option (a) The absolute maximum and minimum occur at critical points and (b) The absolute maximum and minimum occur at the endpoints of the interval are both partially correct. The final answer will depend on the specific cubic function and the interval provided. The correct statement is a combination of (a) and (b), where extrema can occur at the critical points or at the endpoints, but to answer definitively for a general cubic function, we need the specifics of the function, specifically statement (d). Therefore (d) The absolute maximum and minimum cannot be determined without the specific function (f(x)) is the most universally correct option.