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导数的直观理解

导数的直观理解
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2015-07-10 23:26
解析几何导数函数图像
①本范例演示了函数在某一点的切线斜率与导数函数之间的直观联系；②涉及的核心数学概念包括导数、斜率、函数图像；③作图要点——使用了SelectedElement, Circle, Point, Intersect, Segment, Textfield等GeoGebra命令和对象来构建图形；④适合高中数学教学，帮助学生理解导数的几何意义。

GeoGebra 命令及参数

  1. SelectedElement(flist) → f
  2. Circle(Pm4, 0.4) → Cm4
  3. Circle(Pm3, 0.4) → Cm3
  4. Circle(Pm2, 0.4) → Cm2
  5. Circle(Pm1, 0.4) → Cm1
  6. Circle(P0, 0.4) → C0
  7. Circle(P1, 0.4) → C1
  8. Circle(P2, 0.4) → C2
  9. Circle(P3, 0.4) → C3
  10. Circle(P4, 0.4) → C4
  11. Point(Lm3) → Dm3
  12. Point(Lm2) → Dm2
  13. Point(Lm1) → Dm1
  14. Point(L0) → D0
  15. Point(L1) → D1
  16. Point(L2) → D2
  17. Point(L3) → D3
  18. Point(L4) → D4
  19. Point(Lm4) → Dm4
  20. Intersect(Sm4, Cm4, 1) → A
  21. Intersect(Sm4, Cm4, 2) → B
  22. Intersect(Sm3, Cm3) → C, D
  23. Intersect(S4, C4, 1) → E
  24. Intersect(S4, C4, 2) → F
  25. Intersect(S3, C3, 1) → G
  26. Intersect(S3, C3, 2) → H
  27. Intersect(Sm2, Cm2, 1) → I
  28. Intersect(Sm1, Cm1, 2) → J
  29. Intersect(Sm1, Cm1, 1) → K
  30. Intersect(S0, C0, 2) → L
  31. Intersect(S1, C1) → N, O
  32. Intersect(S2, C2, 1) → P
  33. Intersect(S2, C2, 2) → Q
  34. Intersect(Sm2, Cm2, 2) → R
  35. Segment(A, B) → segm4
  36. Segment(D, C) → segm3
  37. Segment(I, R) → segm2
  38. Segment(J, K) → segm1
  39. Segment(O, N) → seg1
  40. Segment(H, G) → seg3
  41. Segment(E, F) → seg4
  42. Intersect(S0, C0, 1) → S
  43. Segment(L, S) → seg0
  44. Segment(P, Q) → seg2
  45. Textfield(user) → inpUser