1. Explaining derivative graphically

Here is f(x) = x^2:

And the derivative of it (2x):

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?

2. Re: Explaining derivative graphically

Originally Posted by daigo
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?
The $\displaystyle x$-values are the same. At the point $\displaystyle (1,1),$ the slope of $\displaystyle f(x) = x^2$ is $\displaystyle f'(1) = 2,$ at $\displaystyle (2,4),$ the slope is $\displaystyle f'(2) = 4$ and so forth.

3. 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.

4. Re: Explaining derivative graphically

Some good examples can be found here.

Derivative - Wikipedia, the free encyclopedia