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Function, Graph, and Table of Variations

Function, Graph, and Table of Variations
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2020-02-07 17:04
FunctionDerivativeIntegral
This example demonstrates a function, its graph, and table of variations. Using GeoGebra commands such as function, derivative, and integral, you can visually understand the properties of the function. The core mathematical concepts involved include functions, derivatives, and integrals. By constructing objects like functions, derivatives, and integrals, you can observe the patterns of function changes. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(G, H, I, J) → poly1, g_1, h_1, i_1, j_1
  2. Point(j_1) → O
  3. Segment(O, P) → t
  4. Point(i_1) → N
  5. Point(g_1) → K
  6. Segment(K, N) → n
  7. Intersect(t, n) → Q
  8. Distance(Q, P) → aa
  9. Min(x(liste1)) → xmin
  10. Segment(Q, P) → a_1
  11. Midpoint(Q, N) → T
  12. Midpoint(T, N) → Z
  13. Max(x(liste1)) → xmax
  14. Function(Polynomial[liste1], xmin, xmax) → f
  15. Derivative(f) → f'
  16. Function(f', xmin, xmax) → g
  17. Function(f1, xmin, xmax) → ff
  18. Function(f2, xmin, xmax) → gg
  19. Vector((xmin, 0), (xmax, 0)) → u
  20. Sequence(Translate[AA, Vector[(i * u)]], i, 0, 1, 0.1) → liste3
  21. Sequence(Segment[Element[liste3, i], Element[liste3, i + 1]], i, 1, Length[liste3]) → liste4
  22. Sequence(Intersect[f', Element[liste4, i]], i, 1, Length[liste4]) → liste2
  23. Sequence(x(Element[liste2, i]), i, 1, Length[liste2]) → liste5
  24. Sequence(f(x(Element[liste2, i])), i, 1, Length[liste2]) → liste6
  25. RemoveUndefined(liste5) → liste7
  26. RemoveUndefined(liste6) → liste8
  27. Sequence((Element[liste7, i], Element[liste8, i]), i, 1, Length[liste7]) → liste9
  28. RemoveUndefined(liste2) → liste2b
  29. Sequence(Segment[Element[liste2b, i], Element[liste9, i]], i, 1, Length[liste7]) → liste10
  30. Segment(AA, (xmin, f(xmin))) → a
  31. Segment(GG, (xmax, f(xmax))) → b
  32. Function(h1, xmin, xmax) → hh1
  33. Function(h2, xmin, xmax) → hh2
  34. Tangent(H_1, f) → c
  35. Circle(H_1, 1.3) → d
  36. Intersect(d, c) → I_1, J_1
  37. Slope(c) → e
  38. Circle(H_1, 4) → k
  39. Intersect(k, c) → K_1, L
  40. Segment(L, K_1) → i
  41. Translate(f', Vector[(0, 0), (0, -8)]) → l_1
  42. Function(l_1, xmin, xmax) → l
  43. Segment((xmin, -8), (xmax, -8)) → j
  44. Sequence(Element[liste2b, i] - (0, 8), i, 1, Length[liste2b]) → liste11
  45. Segment((0, -12), (0, -4)) → m
  46. Function(p, xmin, xmax) → pp
  47. Function(q, xmin, xmax) → qq
  48. Function(-8, xmin, xmax) → r
  49. IntegralBetween(l, r, xmin, xmax) → o
  50. Segment(M, H_1) → s
  51. Slope(c) → z
  52. Point(t) → R
  53. Point(t) → S
  54. Sequence(Q + ((Distance[R, S] * i / Length[liste2b]), 0), i, 0, Length[liste2b]) → liste12
  55. Sequence(x(Element[liste2b, i]), i, 1, Length[liste2b]) → liste13
  56. Sequence(T + ((Distance[R, S] * i / Length[liste2b]), 0), i, 1, Length[liste2b]) → liste15
  57. Vector(AA, N) → u_1
  58. Translate(liste9, u_1) → liste9'
  59. Sequence((x(Element[liste15, i]), y(Element[liste9', i])), i, 1, Length[liste9]) → liste16
  60. Sequence(If[y(Element[liste9, i]) > y(MM), (x(Element[liste15, i]), 4), (x(Element[liste15, i]), -4)], i, 1, Length[liste15]) → liste17
  61. Point(j_1) → A_1
  62. Segment(A_1, B_1) → b_1
  63. Sequence(If[y(Element[liste9, i - 1]) < y(Element[liste9, i]), (x(Element[liste15, i]), 4), (x(Element[liste15, i]), -4)], i, 1, Length[liste15]) → liste19
  64. Sequence(Text["0", Element[liste12, i + 1] - (0.25, 1.5)], i, 1, Length[liste12]) → liste21
  65. Sequence(Midpoint[Element[liste12, i], Element[liste12, i + 1]], i, 1, Length[liste12]) → liste22
  66. Join({{(xmin, f(xmin))}, liste9}) → liste24
  67. Join({{(xmin, f(xmin))}, liste9, {(xmax, f(xmax))}}) → liste26
  68. Sequence(If[y(Element[liste26, i]) < y(Element[liste26, i + 1]), (x(Element[liste15, i]), 4), (x(Element[liste15, i]), -4)], i, 1, Length[liste15]) → liste25
  69. Sequence(Vector[Element[liste25, i], Element[liste25, i + 1]], i, 1, Length[liste26]) → liste18
  70. Vector(V, Element[liste25, 1]) → v_1
  71. Sequence(Text[y(Element[liste9, i]), Element[liste25, i] - (0.75, 0)], i, 1, Length[liste25]) → liste20
  72. Vector(Element[liste25, Length[liste25]], U) → w_1
  73. Sequence(Text[Element[liste13, i], Element[liste12, i + 1] + (-1.5, 0.75)], i, 1, Length[liste2b]) → liste14
  74. Join({{V}, liste25, {U}}) → liste27
  75. PolyLine(liste27) → c_1
  76. Sequence(Segment[Element[liste27, i], Element[liste27, i + 1]], i, 1, Length[liste27]) → liste28
  77. Polygon(C_1, D_1, E_1, F_1) → poly2, c_2, d_1, e_1, f_1
  78. Polygon(C_1, F_1, E_1, D_1) → poly3, c_3, f_2, e_2, d_2
  79. Sequence(If[y(Element[liste26, i - 1]) > y(Element[liste26, i]), Text["+", Element[liste22, i] - (0.25, 1.5)], Text["-", Element[liste22, i] - (0.25, 1.5)]], i, 2, Length[liste22]) → liste23
  80. Line(H_1, yAxis) → m_1
  81. Intersect(m_1, xAxis) → G_1
  82. Segment(H_1, G_1) → n_1
  83. Circle(H_1, 1) → p_1
  84. Intersect(p_1, i) → L_1, M_1
  85. Union({V}, liste25) → poit1
  86. Union(poit1, {U}) → poit2
  87. PolyLine(poit2) → q_1
  88. Segment(Q, P) → r_1
  89. Translate(Q, Vector[((Movement - xmin) / (xmax - xmin) * Vector[Q, P])]) → Q'
  90. Line(Q', yAxis) → s_1
  91. Intersect(s_1, q_1) → N_1
  92. Segment(Q', N_1) → t_1