Understanding derivatives graphically.

[Willowz]

Hi. Doing a bit of self study.

I would like to know how to understand the derivative. I understand the algebra and procedural stuff that you need to do to get the derivative of a function. Is there a way I can understand it graphically?

Say I draw y=x^2 on a graph. Then I draw y=2x on the graph. How are the two related in terms of one being the derivative of the other?

 

[LCKurtz]

Hi. Doing a bit of self study.

I would like to know how to understand the derivative. I understand the algebra and procedural stuff that you need to do to get the derivative of a function. Is there a way I can understand it graphically?

Say I draw y=x^2 on a graph. Then I draw y=2x on the graph. How are the two related in terms of one being the derivative of the other?

Take any value of x, for example x = 1. Draw the line tangent to the parabola at that point. The slope of that tangent line will be the value of the derivative at x = 1: m = 2*1. It works for all values of x. The value of the derivative at a point on a graph is the slope of the tangent line at that point.

 

[Superstring]

I suggest you watch the videos on www.khanacademy.org .