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, and to keep it apart from the rate at a point.
The average rate of change compresses a whole stretch into one number: the slope of the secant line through its endpoints. Shrink the stretch and those averages settle on the rate at a point, and confusing the two is the error this topic exists to prevent. Twelve short steps; press Next for each one.
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?