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Connecting Derivatives and Integrals

Connecting Derivatives and Integrals
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2015-12-26 02:06
CalculusDerivativeIntegral
In collections AP Calculus AB Applet Collection
This example demonstrates how the derivative function is constructed from the slope of the graph of [math]f[/math], and how [math]f[/math] can be reconstructed from the derivative function. Key mathematical concepts include derivatives and integrals. Using GeoGebra commands such as Point, Sequence, and Textfield, the relationship between the function and its derivative can be dynamically observed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Sequence(f(i + inc) - f(i), i, 0, topend, inc) → intheight
  3. Sequence(Segment[(i + inc, 0), (i + inc, (f(i + inc) - f(i)) / inc)], i, 0, topend, inc) → dlines2
  4. Sequence(Segment[(i, 0), (i, (f(i + inc) - f(i)) / inc)], i, 0, topend, inc) → dlines1
  5. Sequence(Segment[(i, 0), (i, f(i))], i, 0, topend, inc) → flines
  6. Sequence((i - inc / 2, Sum[Sequence[intheight(j), j, 1, i / inc]]), i, inc, topend, inc) → intgraph
  7. Sequence(Segment[(i, f(i)), (i + inc, f(i + inc))], i, 0, topend, inc) → fsegs
  8. Sequence(Segment[(i, (f(i + inc) - f(i)) / inc), (i + inc, (f(i + inc) - f(i)) / inc)], i, 0, topend, inc) → dersegs
  9. Textfield(f) → inpF

AI Drawing Prompt Reference

Draw a function f(x) and its derivative and integral graphs. Start by taking a point on the x-axis, then plot the graph of f(x). Next, use the definition of the derivative to draw the derivative segments, and finally use the definition of the integral to draw the integral curve.
The prompt above was compiled from the original drawing commands and is for reference only.