Ace the AP Calculus BC Challenge 2026 – Where Math Meets Mastery!

The average rate of change is the slope of the secant line between x = 1 and x = 3 on the graph of f. It’s given by [f(3) − f(1)] / (3 − 1).

For f(x) = x^2, f(3) = 9 and f(1) = 1. So the average rate of change is (9 − 1) / (2) = 8/2 = 4.

Geometrically, that slope is the rate at which y changes with respect to x on that interval, i.e., the slope of the line through (1,1) and (3,9) is 4.