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函数及其导数的动态演示

函数及其导数的动态演示
几何画板及绘图内容加载中，请稍等……
2017-11-16 01:29
函数导数几何作图滑块动画函数图像
①本范例通过动态演示函数图像及其导数，直观展示函数的局部性质；②涉及核心数学概念包括函数、导数、对称性、菱形、几何变换等；③构造过程中运用了向量、平移、多边形、线段、切线、斜率、表格文本等 GeoGebra 命令与对象；④适合高中及以上学生及数学爱好者用于理解函数分析与几何直观。

GeoGebra 命令及参数

  1. Vector(A_1, C) → u
  2. Vector(A_1, M) → w
  3. Translate(A_1, w) → N
  4. Translate(N, a) → N'_1
  5. Vector(A_1, D) → v
  6. Translate(N, v) → N'
  7. Translate(N', a) → N''
  8. Polygon(A_1, B_1, C_1, D_1) → polygg, a_1, b_1, c_1, d_1
  9. Translate(A_1, u) → E
  10. Translate(B_1, u) → F
  11. Translate(C_1, u) → G
  12. Translate(D_1, u) → H
  13. Translate(A_1, v) → I
  14. Translate(B_1, v) → J
  15. Translate(C_1, v) → K
  16. Translate(D_1, v) → L
  17. Polygon(I, J, K, L) → polygh, i, j, k, l
  18. Translate(I, u) → I'
  19. Translate(J, u) → J'
  20. Translate(K, u) → K'
  21. Translate(L, u) → L'
  22. Polygon(I', J', K', L') → polygf, i', j', k', l'
  23. Translate(B_1, w) → O
  24. Translate(C_1, w) → P
  25. Translate(D_1, w) → Q
  26. Polygon(N, O, P, Q) → polyg, n, o, p, q
  27. Translate(O, v) → O'
  28. Translate(P, v) → P'
  29. Translate(Q, v) → Q'
  30. Polygon(N', O', P', Q') → polys, n', o', p', q'
  31. Translate(O, a) → O'_1
  32. Translate(P, a) → P'_1
  33. Translate(Q, a) → Q'_1
  34. Polygon(N'_1, O'_1, P'_1, Q'_1) → polyf, n'_1, o'_1, p'_1, q'_1
  35. Translate(O', a) → O''
  36. Translate(P', a) → P''
  37. Translate(Q', a) → Q''
  38. Polygon(N'', O'', P'', Q'') → polyh, n'', o'', p'', q''
  39. Segment(R, N'') → c
  40. Segment(H_1, N) → r
  41. Segment(K_1, N'_1) → m_4
  42. Segment(B, N') → d
  43. Segment(O_1, P_1) → j_1
  44. Segment(Q_1, R_1) → k_1
  45. Segment(S_1, T_1) → l_1
  46. Segment(U_1, V_1) → m_1
  47. Segment(W_1, Z_1) → n_1
  48. Segment(A_2, B_2) → p_1
  49. Segment(C_2, D_2) → q_1
  50. Segment(E_2, F_2) → r_1
  51. Segment(G_2, H_2) → s_7
  52. Segment(I_2, J_2) → t_1
  53. Segment(K_2, J_2) → a_2
  54. Polygon(S_1, T_1, V_1, U_1) → poly5, s_8, t_2, v_2, u_2
  55. Polygon(Q_1, R_1, T_1, S_1) → poly6, q_2, r_2, t_3, s_6
  56. Polygon(O_1, P_1, R_1, Q_1) → poly7, o_2, p_2, r_3, q_3
  57. Polygon(U_1, V_1, J_2, K_2) → poly8, u_3, v_3, j_3, k_3
  58. Segment(M_f, P_f) → c_4
  59. Segment(M_f, N_f) → d_4
  60. Tangent(M_f, f) → t_f
  61. Slope(t_f) → k_f
  62. Translate(A_1, u) → E_3
  63. Translate(B_1, u) → F_3
  64. Translate(C_1, u) → G_3
  65. Translate(D_1, u) → H_3
  66. Polygon(E_3, F_3, G_3, H_3) → polygs, e_3, f_6, g_6, h_6
  67. Tangent(M_h, h) → t_h
  68. Segment(P_h, M_h) → b
  69. Segment(M_h, N_h) → e
  70. Slope(t_h) → k_h
  71. Tangent(M_ss, s) → t_s
  72. Slope(t_s) → k_s
  73. Segment(P_s, M_ss) → m
  74. Segment(M_ss, N_s) → e_1
  75. Tangent(M_g, g) → t_g
  76. Slope(t_g) → k_g
  77. Segment(M_g, N_g) → i_1
  78. Segment(M_g, P_g) → b_2
  79. TableText({{A1, B1}, {A2, B2}}, "c_|") → text56
  80. TableText({{A4, B4}, {A5, B5}}, "c_|") → text53
  81. TableText({{A7, B7}, {A8, B8}}, "|_") → text49
  82. TableText({{A10, B10}, {A11, B11}}, "|_") → text46