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Analyticaly vs Numericaly vs Both & A Bit More

    Traditionally (on paper and in books) topics in calc are examined analytically and numerically.


    With communciation now on the web and in digital form, we may use both and a bit more.

    An example of such a digital format is found in a Geometer's Sketchpad at fX.f'X.f''X.intX.gsp

Download Geometer's Sketchpad for Free! at

  1. Edit a function as desired or use the one already on the sheet.
  2. Draw the blue dot on the x-axis to the desired position and note the change in x, function, derivative, and second derivative values.
  3. Select appropriate emoji(s) and move the emoji(s) to mark a desired characteristic of the function.

    Examples and a practice sheet follow.


A harder problem, and answer.

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© 3/16/2023, A. Azzolino