Final answer:
The exact solution for the absolute extrema cannot be determined without the specific function provided. For potential energy functions, extrema are found through first and second derivative tests. For probability functions, extrema are found via areas under curves.
Step-by-step explanation:
Finding the absolute extrema of a function on a closed interval involves several steps which are not provided in the question. However, from the options given, it seems we are evaluating a potential energy function U(x) based on its first and second derivatives. Without the exact function, we cannot definitively choose between options B, C, or D as the correct answer for the minimum and maximum values on the given interval.
If the function mentioned is indeed a potential energy function, then we analyze it by identifying extrema based on the first derivative test and confirming stability with the second derivative test. If the first derivative is zero at a point, it's a candidate for an extremum. The second derivative test then helps determine if the point is a minimum (second derivative positive) or a maximum (second derivative negative).
In cases where the function is a simple horizontal line or a probability distribution, the process differs. For horizontal lines, extrema occur at the endpoints of the interval, whereas probability functions consider areas under curves for their extrema. Without knowing the specific function in the question, we can't proceed with a proper analysis or provide a specific solution.
The question asks us to find the absolute extrema of the function on the closed interval. To do this, we need to analyze the function and find its maximum and minimum values. In this case, the function is not given, so we cannot determine the extrema. Therefore, the correct answer is A) There are no extrema.