Slope: The Derivative of a Function at a Point

[morrowcosom]

Homework Statement

We are calculating the slope of the function f(x) = x2 /3 at x = 2.

For the function f(x) = x2 /3, we now know:

f(2) = 4/3
f(2+h) = (4 + 4h + h^2)/3
Now evaluate the difference quotient, simplifying as much as possible and cancelling h in the denominator:
--------------------------------------------------------------------------------
f(2+h) - f(2)=
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Homework Equations

Slope = lim h->0 [f(x0 + h) - f(x0)] / h

The Attempt at a Solution

{(4+ 4h+ h^2)/3 -4/3} /h
{4+ 4h+ h^2 -4} /h
{4h+ h^2} /h
{h(4+h)} /h
=4+h

I am doing independent study on a computer program and it says my answer is algebraically incorrect. I have gone through the arithmetic many times and cannot find anything incorrect. What am I doing wrong?
(Note: in the next step is where I would just say 4 as the final answer)

 

[fzero]

The Attempt at a Solution

{(4+ 4h+ h^2)/3 -4/3} /h
{4+ 4h+ h^2 -4} /h
{4h+ h^2} /h
{h(4+h)} /h
=4+h
]

You lost the 3 in the denominator in the 2nd step.