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How to draw the derivative for a function?

  1. Sep 26, 2007 #1
    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. jcsd
  3. Sep 27, 2007 #2


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    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.
  4. Sep 27, 2007 #3
    [tex]\frac{\Delta F(P)}{\Delta P}=\frac{F(P+\Delta P)-F(P)}{\Delta P}[/tex]

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