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Math Help - Explaining derivative graphically

  1. #1
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    Explaining derivative graphically

    Here is f(x) = x^2:



    And the derivative of it (2x):



    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?
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    MHF Contributor Reckoner's Avatar
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    Re: Explaining derivative graphically

    Quote Originally Posted by daigo View Post
    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.
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  3. #3
    MHF Contributor ebaines's Avatar
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    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.

    Explaining derivative graphically-slope.jpg
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  4. #4
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    Re: Explaining derivative graphically

    Some good examples can be found here.

    Derivative - Wikipedia, the free encyclopedia
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