How can a point have a slope?

Question

Possible Duplicate:
Approaching to zero, but not equal to zero, then why do the points get overlapped?

You get the derivative of $f(x)$ by getting

the limit as $h$ tends to $0$ of $\dfrac{f(x+h) - f(x)}{(x+h) - (x)}$

I understand that the value of the derivative is the slope of the graph of the function at $x$. However when $h = 0$ you have just one point and you need $2$ points for a slope, don't you?

Answer 1

Note that with one point you cannot just use a formula that uses the rate of change of $x$ because you would divide by zero. That is why we take the limit of $h$ going to zero.