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费马微积分启示

费马微积分启示
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2019-05-16 12:31
微积分导数几何作图
这是一个动态展示费马处理微分和切线方法的范例。通过调整参数，可以观察到不同函数的切线变化。该范例涉及微积分的核心概念，如导数和切线。使用了GeoGebra中的Point, Tangent, Intersect, Min, Dilate, Vector, Segment, Circle, Angle, Rotate, CircleSector, Translate, Polygon等命令。适合高中及以上学生学习微积分。

GeoGebra 命令及参数

  1. Point(c) → A
  2. Tangent(A, c) → f,
  3. Intersect(f_1, Line[D, C]) → N
  4. Intersect(f, xAxis) → B
  5. Min(Distance[B, E], Distance[N, C]) → o
  6. Dilate(E, If[0 < b ≤ 1, 1 - b, 0], A) → E'
  7. Dilate(D, If[0 < b ≤ 1, 1 - b, 0], C) → D'
  8. Vector(E, E') → u
  9. Vector(D, D') → v
  10. Dilate(B, If[1 < b ≤ 2, 2 - b, 0], E) → B'
  11. Segment(B, B') → g
  12. Dilate(E, If[2 < b ≤ 3, 3 - b, 0], D) → E'_1
  13. Segment(E, E'_1) → h
  14. Circle(A, (0.4 * Distance[A, E])) → e
  15. Circle(B, (0.6 * o)) → d
  16. Intersect(d, xAxis) → F, G
  17. Angle(D, B, C) → α
  18. Rotate(G, If[3 < b ≤ 4, ((b - 3) * α), α], B) → G'
  19. CircleSector(B, G, G') → k
  20. Intersect(e, f) → H, I
  21. Rotate(H, If[4 < b ≤ 5, ((b - 4) * (π / 2 - α)), π / 2 - α], A) → H'
  22. CircleSector(A, H, H') → q
  23. Dilate(A, If[6 < b ≤ 7, 7 - b, 0], C) → A'
  24. Vector(A, A') → w
  25. Translate(q, w) → q'
  26. Dilate(B, If[5 < b ≤ 6, 6 - b, 0], E) → B'_1
  27. Intersect(f, i) → J
  28. Polygon(B, B'_1, J) → t1, j, b_1, b'_1
  29. Translate(A, (0, (-Distance[A, E]) - 2)) → A'_1
  30. Translate(E, (0, (-Distance[A, E]) - 2)) → E'_2
  31. Intersect(xAxis, m) → K
  32. Polygon(E, K, A', A) → q1, e_1, k_1, a', a_1
  33. Dilate(A, If[8 < b ≤ 9, 9 - b, 0], A'_1) → A'_2
  34. Vector(A, A'_2) → n
  35. Translate(B, n) → B'_2
  36. Translate(B'_1, n) → L
  37. Translate(J, n) → J'
  38. Polygon(B'_2, L, J') → t1', j', b'_2, l_1
  39. Translate(B, n) → B'_3
  40. Translate(B', n) → B''
  41. Segment(B'_3, B'') → g'
  42. Translate(k, n) → k'
  43. Translate(q, n) → q'_1
  44. Segment(A'_2, B'_2) → r
  45. Vector(B'', A'_2) → s
  46. Dilate(E, If[9 < b ≤ 10, 10 - b, 0], B) → E'_3
  47. Intersect(f, t) → M
  48. Polygon(E'_3, E, A, M) → q2, e'_3, e_2, a_2, m_1
  49. Translate(k, Vector[B]) → k'_1
  50. Dilate(A, If[11 < b ≤ 12, 12 - b, 0], N) → A'_3
  51. Dilate(B, If[11 < b ≤ 12, 12 - b, 0], A) → B'_4
  52. Vector(B, B'_4) → u_1
  53. Translate(k, u_1) → k'_2
  54. Segment(A, A'_3) → g_1
  55. Polygon(A, N, C) → t2, c_1, a_3, n_1
  56. Dilate(B'', If[13 < b ≤ 14, 14 - b, 0], D) → B'''
  57. Vector(B'', B''') → v_1
  58. Translate(A'_2, v_1) → O
  59. Vector(B''', O) → w_1
  60. Dilate(N, If[14 < b ≤ 15, 15 - b, 0], C) → N'
  61. Vector(N, N') → d_1