Mistake Master
Mistake Master · AP Precalculus · Unit 1 · Step-Through Animation
One Number for a Whole Interval
You'll learnto measure a function's average rate of change as the slope of the line joining two points.
The average rate of change compresses an entire stretch into a single number: the slope of the secant line through its endpoints. Shrink the stretch and those averages settle on the rate at a point. Confusing the two is the error this topic exists to prevent.
average rate = rise / run, over the whole interval
Before you start
What you're looking at
A curve with two marked points and the straight secant line drawn between them.
The question
How much does the output change, on average, for each one-unit step of the input across this interval?
Watch for
The rise and the run of the secant — and that the number describes the whole interval, not any single point in it.
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