To estimate the average rate of change of a function \( f(x) \) over the interval \([a, b]\), you can use the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
In this case, you provided the interval \([5.13, 8.77]\). However, to compute the average rate of change, we need a specific function \( f(x) \) to evaluate at the endpoints of the interval (5.13 and 8.77).
If you have a specific function \( f(x) \), please provide it, and I can help you calculate the average rate of change over the given interval. If not, the process is described, and you can apply it once you have a function.