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Definition of Derivative by Jerry Yang

Definition of Derivative by Jerry Yang
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2016-11-23 12:49
FunctionCalculusGeometric Construction
This example demonstrates how to dynamically construct the tangent line of a function to intuitively show the geometric meaning of the derivative. Core math concepts include derivatives, tangent lines, function graphs, and analytical geometry. It uses commands/objects like Line, Parabola, Point, and Tangent from GeoGebra. Suitable for high school and above students learning calculus or for teaching the definition of derivatives.

GeoGebra Commands & Parameters

  1. Line(B, C) → a
  2. Parabola(A, a) → c
  3. Point(c) → D
  4. Point(c) → E
  5. Point(c) → F
  6. Point(c) → G
  7. Point(c) → H
  8. Point(c) → I
  9. Line(D, E) → b
  10. Line(D, F) → d
  11. Line(D, G) → e
  12. Line(D, H) → f
  13. Line(D, I) → g
  14. Tangent(D, c) → h,

AI Drawing Prompt Reference

Draw a parabola with a line through its focus as the directrix. Place several points on the parabola. From one of these points, draw line segments to each of the other points, creating a set of secant lines. Finally, draw the tangent line to the parabola at that same point, contrasting with the secants to show how they approach the tangent, illustrating the geometric meaning of the derivative.
The prompt above was compiled from the original drawing commands and is for reference only.