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Function Variations Demo

Function Variations Demo
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2020-02-01 23:58
FunctionCalculusDerivativeOptimizationGraphing
This example demonstrates dynamic variations of function graphs, highlighting key points like maxima and minima under changing parameters. Core math concepts include function graphs, polynomials, derivatives, linear regression, logarithmic functions, etc. GeoGebra commands and objects used are Max, Min, Polynomial, Function, Sequence, Segment, Point, Tangent, Circle, Intersect, Vector, Line, Join, PolyLine, Polygon, Midpoint. Ideal for high school and above students to explore function properties and dynamic geometric constructions.

GeoGebra Commands & Parameters

  1. Max(Xliste1) → xmax
  2. Min(Xliste1) → xmin
  3. Polynomial(liste1) → f
  4. Function(f, xmin, xmax) → g
  5. Function(g', xmin, xmax) → h
  6. Sequence(Root[h, i], i, xmin, xmax) → liste2
  7. Sequence(g(x(Element[liste2, i])), i, 1, Length[liste2]) → liste3
  8. Sequence((x(Element[liste2, i]), Element[liste3, i]), i, 1, Length[liste2]) → liste4
  9. Unique(liste4) → l2
  10. Unique(liste2) → l1
  11. Sequence((x(Element[l1, i]), m - 4), i, 1, Length[l1]) → liste8b
  12. Sequence(Segment[Element[liste2, i], Element[liste4, i]], i, 1, Length[liste2]) → liste5
  13. Function(gr, xmin, xmax) → grou
  14. Segment((xmin, 0), (xmax, 0)) → a
  15. Max(Yliste1) → Ymax
  16. Segment((xmin, 0), (xmin, g(xmin))) → b
  17. Segment((xmax, 0), (xmax, g(xmax))) → c
  18. Point(liste4) → I
  19. Point(liste4) → K
  20. Segment(J, L) → d
  21. Segment(M, N) → e
  22. Segment(O, P) → i
  23. Sequence((x(Element[liste2, i]), m), i, 1, Length[liste2]) → liste6
  24. Sequence(Segment[Element[liste6, i], Element[liste6, i + 1]], i, 1, Length[liste6]) → liste7
  25. Function(ss, xmin, xmax) → ss1
  26. Sequence(Segment[Element[liste2, i], Element[liste6, i]], i, 1, Length[liste2]) → liste8
  27. Sequence((x(Element[liste2, i]), m - 3), i, 1, Length[liste2]) → liste9
  28. Sequence(Segment[Element[liste4, i], (0, Element[liste3, i])], i, 1, Length[liste2]) → liste10
  29. Segment((xmin, g(xmin)), (0, g(xmin))) → j
  30. Segment((xmax, g(xmax)), (0, g(xmax))) → k
  31. Sequence(Text[Element[XX, i], Element[liste6, i] - (0.3, 0.5)], i, 1, Length[liste6]) → liste11
  32. Tangent(Q, grou) → q
  33. Tangent(Q, g) → l
  34. Circle(Q, n) → p
  35. Intersect(p, l) → R, S
  36. Circle(Q, 1) → c_1
  37. Intersect(c_1, l) → U, V
  38. Segment(U, V) → a_1
  39. Sequence((x(Element[liste8b, i]), m - 4 + (0.5 * y(Element[l2, i]))), i, 1, Length[l2]) → liste6c
  40. Vector(A_1, Element[liste6c, 1]) → w
  41. Vector(Element[liste6c, Length[liste6c]], Z) → z
  42. Segment(U, V) → b_1
  43. Sequence(Vector[Element[liste6c, i], Element[liste6c, i + 1]], i, 1, Length[liste6c]) → liste12
  44. Sequence(Segment[Element[liste6c, i], Element[Unique[liste6], i]], i, 1, Length[liste6c]) → l3
  45. Segment(A_1, Element[liste6c, 1]) → deb
  46. Segment(Element[liste6c, Length[liste6c]], Z) → fina
  47. Line(Q, yAxis) → drit
  48. Intersect(drit, xAxis) → C_1
  49. Intersect(drit, deb) → D_1
  50. Join({{A_1}, liste6c, {Z}}) → tout
  51. PolyLine(tout) → f_1
  52. Intersect(drit, f_1) → E_1
  53. Segment(Q, E_1) → g_1
  54. Sequence(Text[y(Element[l2, i]), Element[liste6c, i] - (0.5, 0.75)], i, 1, Length[liste6c]) → l4
  55. Polygon(F_1, H_1, I_1, G_1) → q1, h_1, i_1, j_1, k_1
  56. Polygon(K_1, J_1, H_1, F_1) → q2, l_1, m_1, n_1, p_1
  57. Polygon(L_1, K_1, F_1, M_1) → q3, q_1, r_1, s_1, t_1
  58. Polygon(M_1, N_1, G_1, F_1) → q4, e_1, f_2, g_2, h_2
  59. Midpoint(K_1, M_1) → O_1
  60. Midpoint(F_1, N_1) → P_1