An average rate compares the change in output with the change in input.
WHAT HAPPENS IF…For a=0 and h=2, what is the average rate?
Interactive exploration
Loading the mathematical model…
Connect the picture to the ideahf(a+h)−f(a)=2a+hfor f(x)=x2,h=0
Expanding (a+h)²−a² gives 2ah+h². Division by h gives 2a+h. The rise/run triangle shows the same calculation geometrically. This experiment uses h>0 so the interval is nondegenerate.
A detail that matters
Average rate is a quotient of changes, not the average of the two function values.