1.2.A.1Concept
The average rate of change of a function over an interval of the function's domain is the constant rate of change that yields the same change in the output values as the function yielded on that interval. It is the ratio of the change in the output values to the change in the input values over that interval.
ExampleAverage rates of change from a table1 / 4
The table gives the height h of a plant, in centimeters, d days after planting. Find the average rate of change of h over [2, 5] and over [5, 9]. On which interval is the plant growing faster?
| d (days) | 0 | 2 | 5 | 9 |
| h (cm) | 3 | 7 | 13 | 31 |
Try it on paper first, then reveal each step to check your work.
Step 1 — Write the formula
Average rate of change over [a, b] = (f(b) − f(a)) / (b − a): the change in output divided by the change in input.