MathPlotAI Logo MathPlotAI

Derivative Exploration by Tom Ahlschwede

Derivative Exploration by Tom Ahlschwede
Loading the math board and drawing, please wait…
2016-09-02 05:48
FunctionCoordinate GeometryDerivativeGeometric Construction
This example demonstrates the dynamic relationship between a function's graph and its derivative, visually showcasing the geometric and physical meanings of derivatives. Core math concepts include derivatives, function graphs, and geometric constructions. It utilizes GeoGebra commands and objects like Point, Circle, Intersect, Segment, and Derivative as outlined in the construction summary. Suitable for high school students and above, or university introductory courses in calculus.

GeoGebra Commands & Parameters

  1. Point(e) → A
  2. Circle(B, 0.8) → k
  3. Intersect(j, k, 1) → C
  4. Intersect(j, k, 2) → D
  5. Segment(C, D) → l
  6. Derivative(f) → f'
  7. Point(h) → E
  8. Circle(F, 0.8) → q
  9. Intersect(p, q, 1) → G
  10. Intersect(p, q, 2) → H
  11. Segment(G, H) → n
  12. Point(g) → I
  13. Circle(J, 0.8) → s
  14. Intersect(r, s, 1) → M
  15. Intersect(r, s, 2) → N
  16. Segment(M, N) → t
  17. Point(i) → K
  18. Circle(L, 0.8) → c_1
  19. Intersect(f_1, c_1, 1) → O
  20. Intersect(f_1, c_1, 2) → P
  21. Segment(O, P) → a_1
  22. Point(b_1) → Q
  23. Circle(R, 0.8) → k_1
  24. Intersect(p_1, k_1, 1) → S
  25. Intersect(p_1, k_1, 2) → T
  26. Segment(S, T) → i_1
  27. Point(d_1) → U
  28. Circle(V, 0.8) → r_1
  29. Intersect(q_1, r_1, 2) → W
  30. Intersect(q_1, r_1, 1) → Z
  31. Segment(Z, W) → j_1
  32. Point(e_1) → A_1
  33. Circle(B_1, 0.8) → t_1
  34. Intersect(s_1, t_1, 2) → C_1
  35. Intersect(s_1, t_1, 1) → D_1
  36. Segment(D_1, C_1) → l_1
  37. Point(g_1) → E_1
  38. Circle(F_1, 0.8) → c_2
  39. Intersect(f_2, c_2, 1) → G_1
  40. Intersect(f_2, c_2, 2) → H_1
  41. Segment(G_1, H_1) → m_1
  42. Point(h_1) → I_1
  43. Circle(J_1, 0.8) → d_2
  44. Intersect(g_2, d_2, 1) → K_1
  45. Intersect(g_2, d_2, 2) → L_1
  46. Segment(K_1, L_1) → n_1