# Explaining derivative graphically

• July 12th 2012, 06:41 AM
daigo
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?
• July 12th 2012, 07:08 AM
Reckoner
Re: Explaining derivative graphically
Quote:

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 $x$-values are the same. At the point $(1,1),$ the slope of $f(x) = x^2$ is $f'(1) = 2,$ at $(2,4),$ the slope is $f'(2) = 4$ and so forth.
• July 12th 2012, 09:21 AM
ebaines
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
• July 12th 2012, 10:27 AM
richard1234
Re: Explaining derivative graphically
Some good examples can be found here.

Derivative - Wikipedia, the free encyclopedia