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An Intuitive Approach to the Derivative

An Intuitive Approach to the Derivative
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2015-07-10 23:26
Coordinate GeometryDerivativeGraphing
This example demonstrates the intuitive connection between the slope of a function at a point and the derivative function. It involves core math concepts like derivatives, slopes, and function graphs. Constructed using GeoGebra commands and objects such as SelectedElement, Circle, Point, Intersect, Segment, and Textfield. Suitable for high school mathematics teaching to help students understand the geometric meaning of derivatives.

GeoGebra Commands & Parameters

  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