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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?

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    @jaques: To be precise, "the slope of the graph" is defined to be "the slope of the tangent line to the graph". The tangent line to the graph is defined in terms of the relative error (see the previous answer I linked to above). The derivative at a point is defined to be the slope of the tangent line to the graph at the point, or equivalently, as the limit above, *because* we can show that this limit, whatever it is, *must* be the slope of the tangent line to the graph at that point.2011-12-03

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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.