find the average rate of change from (2,1) to (8,5) for f(x)=(4x^(2)-2x)/(6x)
average rate is y-change/x-change
(5-1)/(8-2) = 4/6 = 2/3
It doesn't matter what f(x) is. average change just depends on initial and final values for x and y.
Luckily, your interval did not include x=0, where f(x) is undefined.