Question

f(x) = 4x2; x = 2, x = 2 + h

this is telling me to find the average rate of change and the net change? I found one but my answer is disapproved from a friend.

Answer 1

the average rate of change from x=2 to x=2+h is

[f(x+h)-f(x)]/h
= (4(x+h)^2-4x^2)/h
= (4x^2+8xh+4h^2-4x^2)/h
= (8xh+4h^2)/h
= 8x+4h

The net change is just f(x+h)-f(x) = 8xh+4h^2

At x=2, the net change is 16h+4h^2
and the average change is 16+4h