# Thread: Find Average rate of change

1. ## Find Average rate of change

f(x) = x^3 - 4x^2

find the avergae rate of change for x = a and x = a + h

2. ## is this correct?

this is what i got:

2a^3 + 2h^3 + h^3 + 2a^2h - 4a^2 / h

3. Originally Posted by needhelp75
f(x) = x^3 - 4x^2

find the avergae rate of change for x = a and x = a + h
The average rate of change is given by $\frac{f(a + h) - f(a)}{h}$.

$f(a+h) = (a + h)^3 - 4(a + h)^2$

$= a^3 + 3a^2h + 3ah^2 + h^3 - 4a^2 - 8ah -4h^2$

$f(a) = a^3 - 4a^2$

$f(a+h) - f(a) = 3a^2h + 3ah^2 + h^3 - 8ah - 4h^2$

$\frac{f(a+h) - f(a)}{h} = 3a^2 + 3ah + h^2 - 8a - 4h$.

4. thank you
you = win + genius

5. Originally Posted by needhelp75
thank you
you = win + genius
Thanks :P

Before I teach calculus, I teach them the Binomial Theorem, so they can expand expressions like $(a + h)^n$.

If it helps, Binomial theorem - Wikipedia, the free encyclopedia