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导数构建：函数与导数图像的关系

导数构建：函数与导数图像的关系
几何画板及绘图内容加载中，请稍等……
2015-09-14 06:20
函数导数几何作图
本范例通过GeoGebra动态演示函数与其导数图像的关系，帮助学生直观理解导数的几何意义。核心数学概念包括导数定义、函数图像变换及几何作图。作图要点涉及使用Element、Corner、Point等GeoGebra命令构建函数与导数曲线。适合高中生学习微积分基础，或用于数学教学辅助。

GeoGebra 命令及参数

  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 绘图提示语参考

绘制一个动态演示函数与其导数关系的图形。从函数列表中选择一个函数，在绘图区显示其图像。在函数图像上等间距取一系列点，并在每个点处绘制一条与函数图像相交的短线段，这些线段的方向和长度由该点的函数值决定，用于近似表示该点的导数。同时，在另一区域绘制这些点对应的导数值，形成导函数图像。通过控制参数调整线段长度和显示状态，直观展示导数作为切线斜率的概念。
以上提示语为根据原始绘图命令整理而来，仅供参考。