World 1 · Functions & Limits · 7 minAverage rate of change
The secant line
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Between two points on a curve, the average rate of change is just the slope of the straight line joining them — the secant. It answers "on average, how fast did the output change across this interval?"
Formula: (f(b) − f(a)) / (b − a). It is rise over run again, now for a curve. On a distance-vs-time graph this average rate is your average speed over the trip.
Check yourself
The average rate of change of f on [a,b] is…
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