How to draw the derivative for a function?

1. Sep 26, 2007

MIA6

If you see a graph of a function, then you need to draw the derivative for this function. How can you draw it? I know you have to find some points, and find their slopes, and then put it on the graph and connect the points, but how can I estimate the slopes. I can only figure out the slope of 0 and positive slope or negative slope. Other than that, I can't tell the slope. Hope you can tell me.
Thanks for help.

2. Sep 27, 2007

EnumaElish

The derivative at point (x,y) is the slope of the line tangent to the function at (x,y). I think you are concentrating too much on the function itself. Instead try visualizing a straight line that "barely" touches the function at point (x,y). Then calculate the slope of that tangent line.

3. Sep 27, 2007

ice109

$$\frac{\Delta F(P)}{\Delta P}=\frac{F(P+\Delta P)-F(P)}{\Delta P}$$

there the slope of the line that connects point (F,P) and (F(P+ΔP),P+ΔP). now what happens when ΔP approaches zero?