Final answer:
To find the interval with a negative average rate of change for function f(x), look for parts of its graph where f(x) decreases as x increases, typically represented by a downward slope on the graph.
Step-by-step explanation:
To determine over which interval the function f(x) has a negative average rate of change, we should look for the portion of the graph where the function's value decreases over time. A negative average rate of change implies that, as x increases, the f(x) values decrease, which graphically would be represented by a downward slope. From the given information, we could deduce this behavior from graphs showing a straight line with a negative slope or a parabolic curve opening downwards. Specific details like the current falling to a certain value over time intervals or the description of a spring force curve f(x) = -kx can indicate intervals of negative rates.
In chemistry, a negative slope in the context of reaction rates typically represents a decreasing reaction rate. In physics, the mention of negative acceleration corresponds with the notion of decreasing velocity. For population dynamics, negative feedback mechanisms impacting growth rates can lead to a decrease over time as well. Without a graph or additional context, it is difficult to provide a pinpointed interval. However, the student should graph the function (if not already provided) and look for intervals where the function is decreasing, which would be where the negative average rate of change is found.