Explaining derivative graphically

Here is f(x) = x^2:

http://i.imgur.com/YT7CF.png

And the derivative of it (2x):

http://i.imgur.com/seDFz.png

So each point on the slope of the derivative is supposed to represent the slope of the line tangent at a certain point on the original function.

Say I choose an x-value on the derivative 1, so the point on the line would be (1,2).

Where on the original function would this be the represented slope of? As I understand it, the x-value 1 corresponds with a slope of 2, the x-value 2 corresponds with a slope of 4, etc. but how do I find the point on the original function where these are the slopes of?

Re: Explaining derivative graphically

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Re: Explaining derivative graphically

To reinforce what Reckoner said - the attached figure shows the tangent line for the parabola at (1,1), and note that it's slope at that point is 2.

Attachment 24273

Re: Explaining derivative graphically