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Dynamic Demo of Functions and Their Derivatives

Dynamic Demo of Functions and Their Derivatives
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2017-11-16 01:29
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This example dynamically demonstrates function graphs and their derivatives, visually showcasing local properties of functions. It involves core math concepts like functions, derivatives, symmetry, rhombus, and geometric transformations. GeoGebra commands and objects used include Vector, Translate, Polygon, Segment, Tangent, Slope, TableText, and various objects like K_1, C, M, etc. Suitable for high school students and math enthusiasts to understand function analysis and geometric intuition.

GeoGebra Commands & Parameters

  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