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Understanding derivatives graphically.

  1. Jun 25, 2011 #1
    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?
  2. jcsd
  3. Jun 25, 2011 #2


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    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.
  4. Jun 25, 2011 #3
    I suggest you watch the videos on www.khanacademy.org .
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