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

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

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- Dec 15th 2008, 09:30 PMneedhelp75Find Average rate of change
f(x) = x^3 - 4x^2

find the avergae rate of change for x = a and x = a + h - Dec 15th 2008, 09:48 PMneedhelp75is this correct?
this is what i got:

2a^3 + 2h^3 + h^3 + 2a^2h - 4a^2 / h - Dec 15th 2008, 11:28 PMProve It
The average rate of change is given by $\displaystyle \frac{f(a + h) - f(a)}{h}$.

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

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

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

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

$\displaystyle \frac{f(a+h) - f(a)}{h} = 3a^2 + 3ah + h^2 - 8a - 4h$. - Dec 15th 2008, 11:43 PMneedhelp75
thank you

you = win + genius(Clapping) - Dec 16th 2008, 09:44 PMProve It
Thanks :P

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

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