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Derivative Builder by Gail Neal

Derivative Builder by Gail Neal
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2016-06-28 21:54
FunctionCalculusDerivative
This example demonstrates the relationship between a function and the graph of its derivative. It involves core math concepts like derivatives, polynomial functions, and indefinite integrals. Construction highlights include using GeoGebra commands and objects such as Element, Corner, Point, If, Segment, and Textfield. Ideal for high school mathematics education to help students visually understand the geometric meaning of derivatives and original functions.

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'