Final answer:
The average rate of change of a function over an interval is calculated as the difference of function values divided by the difference in points. The instantaneous rate of change corresponds to the slope of a tangent line at that point and they are equal at least once according to the Mean Value Theorem, but specific details about the function are required to determine the exact number.
Step-by-step explanation:
To calculate the average rate of change of f over the interval [-2.5, 6], we typically need the value of the function f at these two points. The average rate of change is found by using the formula: Average Rate of Change = (f(6) - f(-2.5)) / (6 - (-2.5)). However, without the specific function f, we cannot compute an exact value. Nevertheless, we can still discuss the concepts.
The instantaneous rate of change of f at a point is the slope of the tangent to the curve at that point. According to the Mean Value Theorem in calculus, if the function f is continuous on the closed interval and differentiable on the open interval (-2.5, 6), then there is at least one point c in the interval where the instantaneous rate of change of f (the derivative f'(c)) is equal to the average rate of change over the entire interval. Thus, there is at least one such point where they are equal.
Further details about the function or its graph would be required to determine precisely how many times the instantaneous and average rates are equal within the given interval.