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Derivative Builder

Derivative Builder
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2016-06-28 22:29
Coordinate GeometryCalculusGeometric Construction
This example demonstrates how to visualize the concept of derivatives dynamically by constructing points, segments, and text fields. Core math concepts include derivatives, coordinate geometry, arithmetic operations, and scalene triangles. Construction highlights from the summary involve commands like Corner, Point, If, Segment, and Textfield. Suitable for high school and above students to learn and understand the calculation and geometric meaning of derivatives in calculus.

GeoGebra Commands & Parameters

  1. Corner(3) → c3
  2. Corner(1) → c1
  3. Point(x = B2) → C2
  4. Point(x = B3) → C3
  5. Point(x = B4) → C4
  6. Point(x = B5) → C5
  7. Point(x = B6) → C6
  8. Point(x = B7) → C7
  9. Point(x = B8) → C8
  10. Point(x = B9) → C9
  11. Point(x = B10) → C10
  12. Point(x = B11) → C11
  13. Point(x = B12) → C12
  14. Point(x = B13) → C13
  15. Point(x = B14) → C14
  16. Point(x = B15) → C15
  17. Point(x = B16) → C16
  18. Point(x = B17) → C17
  19. Point(x = B18) → C18
  20. Point(x = B19) → C19
  21. Point(x = B20) → C20
  22. If(togfp ≟ 0, "Show f'(x)", "Hide f'(x)") → ShowHidefprime
  23. Segment(D2 + ((h * delx / 2) * (1, y(C2))), D2 - ((h * delx / 2) * (1, y(C2)))) → E2
  24. Segment(D3 + ((h * delx / 2) * (1, y(C3))), D3 - ((h * delx / 2) * (1, y(C3)))) → E3
  25. Textfield(f) → InputfOFx
  26. Segment(D4 + ((h * delx / 2) * (1, y(C4))), D4 - ((h * delx / 2) * (1, y(C4)))) → E4
  27. Segment(D5 + ((h * delx / 2) * (1, y(C5))), D5 - ((h * delx / 2) * (1, y(C5)))) → E5
  28. Segment(D6 + ((h * delx / 2) * (1, y(C6))), D6 - ((h * delx / 2) * (1, y(C6)))) → E6
  29. Segment(D7 + ((h * delx / 2) * (1, y(C7))), D7 - ((h * delx / 2) * (1, y(C7)))) → E7
  30. Segment(D8 + ((h * delx / 2) * (1, y(C8))), D8 - ((h * delx / 2) * (1, y(C8)))) → E8
  31. Segment(D9 + ((h * delx / 2) * (1, y(C9))), D9 - ((h * delx / 2) * (1, y(C9)))) → E9
  32. Segment(D10 + ((h * delx / 2) * (1, y(C10))), D10 - ((h * delx / 2) * (1, y(C10)))) → E10
  33. Segment(D11 + ((h * delx / 2) * (1, y(C11))), D11 - ((h * delx / 2) * (1, y(C11)))) → E11
  34. Segment(D12 + ((h * delx / 2) * (1, y(C12))), D12 - ((h * delx / 2) * (1, y(C12)))) → E12
  35. Segment(D13 + ((h * delx / 2) * (1, y(C13))), D13 - ((h * delx / 2) * (1, y(C13)))) → E13
  36. Segment(D14 + ((h * delx / 2) * (1, y(C14))), D14 - ((h * delx / 2) * (1, y(C14)))) → E14
  37. Segment(D15 + ((h * delx / 2) * (1, y(C15))), D15 - ((h * delx / 2) * (1, y(C15)))) → E15
  38. Segment(D16 + ((h * delx / 2) * (1, y(C16))), D16 - ((h * delx / 2) * (1, y(C16)))) → E16
  39. Segment(D17 + ((h * delx / 2) * (1, y(C17))), D17 - ((h * delx / 2) * (1, y(C17)))) → E17
  40. Segment(D18 + ((h * delx / 2) * (1, y(C18))), D18 - ((h * delx / 2) * (1, y(C18)))) → E18
  41. Segment(D19 + ((h * delx / 2) * (1, y(C19))), D19 - ((h * delx / 2) * (1, y(C19)))) → E19
  42. Segment(D20 + ((h * delx / 2) * (1, y(C20))), D20 - ((h * delx / 2) * (1, y(C20)))) → E20
  43. Point(x = B1) → C1
  44. Segment(D1 + ((h * delx / 2) * (1, y(C1))), D1 - ((h * delx / 2) * (1, y(C1)))) → E1
  45. Textfield(g) → InputGuess

AI Drawing Prompt Reference

Create a dynamic derivative visualization: place an editable function input field and a guess input field on the coordinate plane, along with a toggle button to show or hide the derivative curve. Sample a series of equally spaced points along the function curve, and from each point draw a short horizontal segment whose length is controlled by a parameter, representing the differential increment at that point. Also include corner reference points for orientation. The layout should clearly display the function curve, sampled points, and their corresponding horizontal tangent segments to illustrate how the derivative changes with position.
The prompt above was compiled from the original drawing commands and is for reference only.