Calculate the average rate of change for
f(x) = 8x2 + 4x
from x to x + h.
f(x) = 8x^2 + 4x
f(x+h) = 8(x+h)^2 + 4(x+h)
= 8x^2 + 16xh + 8h^2 + 4x + 4h
average rate of change
= (8x^2 + 16xh + 8h^2 + 4x + 4h - (8x^2 + 4x))/(x+h - x)
= (16xh + 8h^2 + 4h)/h
= 16x + 8h + 4 , h ≠ 0