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Derivative Builder: Function and Derivative Graph Relationship

Derivative Builder: Function and Derivative Graph Relationship
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2015-09-14 06:20
FunctionDerivativeGeometric Construction
This example dynamically demonstrates the relationship between a function and its derivative using GeoGebra, helping students visualize the geometric meaning of derivatives. Key mathematical concepts include derivative definition, function graph transformations, and geometric construction. Construction involves using commands like Element, Corner, Point, and others. Suitable for high school students learning calculus fundamentals or for math teaching support.

GeoGebra Commands & Parameters

  1. Element(flist, SelectedIndex[fNameList]) → f
  2. Corner(3) → c3
  3. Corner(1) → c1
  4. Point(x = B1) → C1
  5. Point(x = B2) → C2
  6. Point(x = B3) → C3
  7. Point(x = B4) → C4
  8. Point(x = B5) → C5
  9. Point(x = B6) → C6
  10. Point(x = B7) → C7
  11. Point(x = B8) → C8
  12. Point(x = B9) → C9
  13. Point(x = B10) → C10
  14. Point(x = B11) → C11
  15. Point(x = B12) → C12
  16. Point(x = B13) → C13
  17. Point(x = B14) → C14
  18. Point(x = B15) → C15
  19. Point(x = B16) → C16
  20. Point(x = B17) → C17
  21. Point(x = B18) → C18
  22. Point(x = B19) → C19
  23. Point(x = B20) → C20
  24. If(togfp ≟ 0, "Show f'(x)", "Hide f'(x)") → ShowHidefprime
  25. Segment(D1 + ((h * delx / 2) * (1, y(C1))), D1 - ((h * delx / 2) * (1, y(C1)))) → E1
  26. Segment(D2 + ((h * delx / 2) * (1, y(C2))), D2 - ((h * delx / 2) * (1, y(C2)))) → E2
  27. Segment(D3 + ((h * delx / 2) * (1, y(C3))), D3 - ((h * delx / 2) * (1, y(C3)))) → E3
  28. Segment(D4 + ((h * delx / 2) * (1, y(C4))), D4 - ((h * delx / 2) * (1, y(C4)))) → E4
  29. Segment(D5 + ((h * delx / 2) * (1, y(C5))), D5 - ((h * delx / 2) * (1, y(C5)))) → E5
  30. Segment(D6 + ((h * delx / 2) * (1, y(C6))), D6 - ((h * delx / 2) * (1, y(C6)))) → E6
  31. Segment(D7 + ((h * delx / 2) * (1, y(C7))), D7 - ((h * delx / 2) * (1, y(C7)))) → E7
  32. Segment(D8 + ((h * delx / 2) * (1, y(C8))), D8 - ((h * delx / 2) * (1, y(C8)))) → E8
  33. Segment(D9 + ((h * delx / 2) * (1, y(C9))), D9 - ((h * delx / 2) * (1, y(C9)))) → E9
  34. Segment(D10 + ((h * delx / 2) * (1, y(C10))), D10 - ((h * delx / 2) * (1, y(C10)))) → E10
  35. Segment(D11 + ((h * delx / 2) * (1, y(C11))), D11 - ((h * delx / 2) * (1, y(C11)))) → E11
  36. Segment(D12 + ((h * delx / 2) * (1, y(C12))), D12 - ((h * delx / 2) * (1, y(C12)))) → E12
  37. Segment(D13 + ((h * delx / 2) * (1, y(C13))), D13 - ((h * delx / 2) * (1, y(C13)))) → E13
  38. Segment(D14 + ((h * delx / 2) * (1, y(C14))), D14 - ((h * delx / 2) * (1, y(C14)))) → E14
  39. Segment(D15 + ((h * delx / 2) * (1, y(C15))), D15 - ((h * delx / 2) * (1, y(C15)))) → E15
  40. Segment(D16 + ((h * delx / 2) * (1, y(C16))), D16 - ((h * delx / 2) * (1, y(C16)))) → E16
  41. Segment(D17 + ((h * delx / 2) * (1, y(C17))), D17 - ((h * delx / 2) * (1, y(C17)))) → E17
  42. Segment(D18 + ((h * delx / 2) * (1, y(C18))), D18 - ((h * delx / 2) * (1, y(C18)))) → E18
  43. Segment(D19 + ((h * delx / 2) * (1, y(C19))), D19 - ((h * delx / 2) * (1, y(C19)))) → E19
  44. Segment(D20 + ((h * delx / 2) * (1, y(C20))), D20 - ((h * delx / 2) * (1, y(C20)))) → E20
  45. Point(x = B21) → C21
  46. Segment(D21 + ((h * delx / 2) * (1, y(C21))), D21 - ((h * delx / 2) * (1, y(C21)))) → E21
  47. Point(x = B22) → C22
  48. Segment(D22 + ((h * delx / 2) * (1, y(C22))), D22 - ((h * delx / 2) * (1, y(C22)))) → E22
  49. Point(x = B23) → C23
  50. Segment(D23 + ((h * delx / 2) * (1, y(C23))), D23 - ((h * delx / 2) * (1, y(C23)))) → E23
  51. Point(x = B24) → C24
  52. Segment(D24 + ((h * delx / 2) * (1, y(C24))), D24 - ((h * delx / 2) * (1, y(C24)))) → E24
  53. Point(x = B25) → C25
  54. Segment(D25 + ((h * delx / 2) * (1, y(C25))), D25 - ((h * delx / 2) * (1, y(C25)))) → E25
  55. Point(x = B26) → C26
  56. Segment(D26 + ((h * delx / 2) * (1, y(C26))), D26 - ((h * delx / 2) * (1, y(C26)))) → E26
  57. Point(x = B27) → C27
  58. Segment(D27 + ((h * delx / 2) * (1, y(C27))), D27 - ((h * delx / 2) * (1, y(C27)))) → E27
  59. Point(x = B28) → C28
  60. Segment(D28 + ((h * delx / 2) * (1, y(C28))), D28 - ((h * delx / 2) * (1, y(C28)))) → E28
  61. Point(x = B29) → C29
  62. Segment(D29 + ((h * delx / 2) * (1, y(C29))), D29 - ((h * delx / 2) * (1, y(C29)))) → E29
  63. Point(x = B30) → C30
  64. Segment(D30 + ((h * delx / 2) * (1, y(C30))), D30 - ((h * delx / 2) * (1, y(C30)))) → E30
  65. Textfield(f6) → Inputf
  66. Element(fPrimeList, SelectedIndex[fNameList]) → f'

AI Drawing Prompt Reference

Create a dynamic visualization showing the relationship between a function and its derivative. Plot a selected function curve. Place a series of equally spaced points along the curve)Skip. At each point, draw a short line segment centered on the point, with its length proportional to the function value at that point, representing the derivative. Additionally, plot the derivative values as a separate curve. Include controls to adjust the segment length and toggle the derivative display, illustrating the geometric meaning of the derivative as the slope of the tangent.
The prompt above was compiled from the original drawing commands and is for reference only.