Final answer:
Without the specific function f(x), we cannot definitively determine the interval where the average rate of change is zero among the provided options. The average rate of change is zero when a function's values are the same at both the start and end of an interval.
Step-by-step explanation:
The question relates to finding the interval over which the average rate of change of a function f(x) is zero. To have an average rate of change of zero, the value of the function at the beginning and end of the interval must be the same, because the average rate of change is computed as the change in the function's value divided by the change in x (which would be zero if the function's values are the same at both ends of the interval).
Reviewing the provided excerpts and using the principle that an average velocity or rate of change is zero if the start and end values are the same, or if the function returns to its initial value after increasing and decreasing (as implied by d. His average velocity is zero because the velocity of each successive lap is equal and opposite), we can determine the correct interval. However, without the specific function f(x) given, we cannot definitively determine the correct interval among the provided options A) 2 < x < 3, B) -5 < x < 5, C) -1 < x < 2, D) -3 < x < -2 solely from the excerpts.