# How can a point have a slope? [duplicate]

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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## marked as duplicate by Henning Makholm, Srivatsan, Asaf Karagila, Guess who it is., t.b.Dec 4 '11 at 1:57

Which is why we take the limit rather than taking $h=0$. –  Thomas Andrews Dec 3 '11 at 22:56
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.