The average rate of change of a function over an interval [a, b] is found using the formula:

Average Rate of Change=f(b)−f(a)b−a\text{Average Rate of Change}=\frac{f(b)-f(a)}{b-a}Average Rate of Change=b−af(b)−f(a)​

Here, f(a)f(a)f(a) and f(b)f(b)f(b) are the values of the function at the endpoints a and b, respectively. Essentially, this formula calculates the ratio of the change in the function's output values to the change in the input values over the interval. This concept is the same as calculating the slope between two points on the function's graph. To find it step-by-step:

1. Evaluate the function at the start of the interval: f(a)f(a)f(a).
2. Evaluate the function at the end of the interval: f(b)f(b)f(b).
3. Subtract the values: f(b)−f(a)f(b)-f(a)f(b)−f(a).
4. Subtract the input values: b−ab-ab−a.
5. Divide the changes: f(b)−f(a)b−a\frac{f(b)-f(a)}{b-a}b−af(b)−f(a)​.

This gives the average rate at which the function changes per unit change in the input over the interval [a, b].