Calculating Average Rate of Change

Pre-Calculus · Axiom Academy

EXAMPLE Calculating Average Rate of Change Find the slope of the secant line between two points on a curve Find the average rate of change of f(x) = x^2 - 2x + 3 on the interval . It is the slope of the secant line joining and . The average rate of change equals the slope of the secant line (orange). Over the run of 3 the function climbs a rise of 9 , so the slope is . Nice work — you computed an average rate of change from start to finish. It is a slope: the average rate of change is the slope of the secant line through and . The formula: — change in output over change in input. This result: on , f rises from 2 to 11 , giving . Read the sign: a positive value means the function increases on average; a negative one means it decreases. Shrink the interval toward a single point and this secant slope becomes the instantaneous rate of change — the idea behind the derivative.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.