积极 AI Logo 积极 AI

导数初步原理演示

导数初步原理演示
几何画板及绘图内容加载中，请稍等……
2020-03-16 18:20
函数解析几何导数几何作图
①本范例通过动态图形演示导数的几何意义，即函数在某点的切线斜率；②涉及核心数学概念包括导数定义、极限思想、函数图像、切线斜率；③构造过程中运用了 GeoGebra 命令如 Sequence（序列）、OrthogonalLine（垂线）、Intersect（交点）、Segment（线段）、Angle（角度）、Point（点）、If（条件判断）、Midpoint（中点）；④适合高中及以上学生学习微积分入门知识，或用于理解导数与函数图像的关系。

GeoGebra 命令及参数

  1. Sequence(u - x(A), u, b, q, -0.1) → List
  2. OrthogonalLine(B, xAxis) → i
  3. Intersect(i, xAxis) → C
  4. OrthogonalLine(A, xAxis) → j
  5. Intersect(j, xAxis) → D
  6. OrthogonalLine(B, yAxis) → k
  7. Intersect(k, yAxis) → F
  8. OrthogonalLine(A, yAxis) → l
  9. Intersect(l, yAxis) → E
  10. Intersect(i, l) → G
  11. Segment(B, C) → r
  12. Segment(A, D) → s
  13. Segment(G, E) → t
  14. Segment(B, F) → d
  15. Angle(G, A, B) → α
  16. Segment(A, G) → m_1
  17. Segment(B, G) → n
  18. Point(xAxis) → H
  19. Point(xAxis) → I
  20. Segment(H, I) → f_1
  21. Point(yAxis) → J
  22. Point(yAxis) → K
  23. Segment(J, K) → g_1
  24. Segment(E, A) → h_1
  25. Sequence(f(z) - y(A), z, b, q, -0.1) → L_1
  26. If(q ≤ 3, Element[L_1, 1] + "", "") → C3
  27. If(q ≤ 2.9, Element[L_1, 2] + "", "") → C4
  28. If(q ≤ 2.8, Element[L_1, 3] + "", "") → C5
  29. If(q ≤ 2.7, Element[L_1, 4] + "", "") → C6
  30. If(q ≤ 2.6, Element[L_1, 5] + "", "") → C7
  31. If(q ≤ 2.5, Element[L_1, 6] + "", "") → C8
  32. If(q ≤ 2.4, Element[L_1, 7] + "", "") → C9
  33. If(q ≤ 2.3, Element[L_1, 8] + "", "") → C10
  34. If(q ≤ 2.2, Element[L_1, 9] + "", "") → C11
  35. If(q ≤ 2.1, Element[L_1, 10] + "", "") → C12
  36. If(q ≤ 2, Element[L_1, 11] + "", "") → C13
  37. If(q ≤ 1.9, Element[L_1, 12] + "", "") → C14
  38. If(q ≤ 1.8, Element[L_1, 13] + "", "") → C15
  39. If(q ≤ 1.7, Element[L_1, 14] + "", "") → C16
  40. If(q ≤ 1.6, Element[L_1, 15] + "", "") → C17
  41. If(q ≤ 1.5, Element[L_1, 16] + "", "") → C18
  42. If(q ≤ 1.4, Element[L_1, 17] + "", "") → C19
  43. If(q ≤ 1.3, Element[L_1, 18] + "", "") → C20
  44. If(q ≤ 1.2, Element[L_1, 19] + "", "") → C21
  45. If(q ≤ 1.1, Element[L_1, 20] + "", "") → C22
  46. If(q ≤ 3, Element[List, 1]) → H3
  47. If(q ≤ 2.9, Element[List, 2]) → H4
  48. If(q ≤ 2.8, Element[List, 3]) → H5
  49. If(q ≤ 2.7, Element[List, 4]) → H6
  50. If(q ≤ 2.6, Element[List, 5]) → H7
  51. If(q ≤ 2.5, Element[List, 6]) → H8
  52. If(q ≤ 2.4, Element[List, 7]) → H9
  53. If(q ≤ 2.3, Element[List, 8]) → H10
  54. If(q ≤ 2.2, Element[List, 9]) → H11
  55. If(q ≤ 2.1, Element[List, 10]) → H12
  56. If(q ≤ 2, Element[List, 11]) → H13
  57. If(q ≤ 1.9, Element[List, 12]) → H14
  58. If(q ≤ 1.8, Element[List, 13]) → H15
  59. If(q ≤ 1.7, Element[List, 14]) → H16
  60. If(q ≤ 1.6, Element[List, 15]) → H17
  61. If(q ≤ 1.5, Element[List, 16]) → H18
  62. If(q ≤ 1.4, Element[List, 17]) → H19
  63. If(q ≤ 1.3, Element[List, 18]) → H20
  64. If(q ≤ 1.2, Element[List, 19]) → H21
  65. If(q ≤ 1.1, Element[List, 20]) → H22
  66. If(q ≤ 3, Element[L_1, 1]) → I3
  67. If(q ≤ 2.9, Element[L_1, 2]) → I4
  68. If(q ≤ 2.8, Element[L_1, 3]) → I5
  69. If(q ≤ 2.7, Element[L_1, 4]) → I6
  70. If(q ≤ 2.6, Element[L_1, 5]) → I7
  71. If(q ≤ 2.5, Element[L_1, 6]) → I8
  72. If(q ≤ 2.4, Element[L_1, 7]) → I9
  73. If(q ≤ 2.3, Element[L_1, 8]) → I10
  74. If(q ≤ 2.2, Element[L_1, 9]) → I11
  75. If(q ≤ 2.1, Element[L_1, 10]) → I12
  76. If(q ≤ 2, Element[L_1, 11]) → I13
  77. If(q ≤ 1.9, Element[L_1, 12]) → I14
  78. If(q ≤ 1.8, Element[L_1, 13]) → I15
  79. If(q ≤ 1.7, Element[L_1, 14]) → I16
  80. If(q ≤ 1.6, Element[L_1, 15]) → I17
  81. If(q ≤ 1.5, Element[L_1, 16]) → I18
  82. If(q ≤ 1.4, Element[L_1, 17]) → I19
  83. If(q ≤ 1.3, Element[L_1, 18]) → I20
  84. If(q ≤ 1.2, Element[L_1, 19]) → I21
  85. If(q ≤ 1.1, Element[L_1, 20]) → I22
  86. If(q ≤ 2.3, I10 / H10 + "", "") → E10
  87. If(q ≤ 1.9, Element[List, 12] + "", "") → D14
  88. If(q ≤ 3, Element[List, 1] + "", "") → D3
  89. If(q ≤ 2.9, Element[List, 2] + "", "") → D4
  90. If(q ≤ 2.8, Element[List, 3] + "", "") → D5
  91. If(q ≤ 2.7, Element[List, 4] + "", "") → D6
  92. If(q ≤ 2.6, Element[List, 5] + "", "") → D7
  93. If(q ≤ 2.5, Element[List, 6] + "", "") → D8
  94. If(q ≤ 2.4, Element[List, 7] + "", "") → D9
  95. If(q ≤ 2.3, Element[List, 8] + "", "") → D10
  96. If(q ≤ 2.2, Element[List, 9] + "", "") → D11
  97. If(q ≤ 2.1, Element[List, 10] + "", "") → D12
  98. If(q ≤ 2, Element[List, 11] + "", "") → D13
  99. If(q ≤ 1.8, Element[List, 13] + "", "") → D15
  100. If(q ≤ 1.7, Element[List, 14] + "", "") → D16
  101. If(q ≤ 1.6, Element[List, 15] + "", "") → D17
  102. If(q ≤ 1.5, Element[List, 16] + "", "") → D18
  103. If(q ≤ 1.4, Element[List, 17] + "", "") → D19
  104. If(q ≤ 1.3, Element[List, 18] + "", "") → D20
  105. If(q ≤ 1.2, Element[List, 19] + "", "") → D21
  106. If(q ≤ 1.1, Element[List, 20] + "", "") → D22
  107. If(q ≤ 3, I3 / H3 + "", "") → E3
  108. If(q ≤ 2.9, I4 / H4 + "", "") → E4
  109. If(q ≤ 2.8, I5 / H5 + "", "") → E5
  110. If(q ≤ 2.7, I6 / H6 + "", "") → E6
  111. If(q ≤ 2.6, I7 / H7 + "", "") → E7
  112. If(q ≤ 2.5, I8 / H8 + "", "") → E8
  113. If(q ≤ 2.4, I9 / H9 + "", "") → E9
  114. If(q ≤ 2.2, I11 / H11 + "", "") → E11
  115. If(q ≤ 2.1, I12 / H12 + "", "") → E12
  116. If(q ≤ 2, I13 / H13 + "", "") → E13
  117. If(q ≤ 1.9, I14 / H14 + "", "") → E14
  118. If(q ≤ 1.8, I15 / H15 + "", "") → E15
  119. If(q ≤ 1.7, I16 / H16 + "", "") → E16
  120. If(q ≤ 1.6, I17 / H17 + "", "") → E17
  121. If(q ≤ 1.5, I18 / H18 + "", "") → E18
  122. If(q ≤ 1.4, I19 / H19 + "", "") → E19
  123. If(q ≤ 1.3, I20 / H20 + "", "") → E20
  124. If(q ≤ 1.2, I21 / H21 + "", "") → E21
  125. If(q ≤ 1.1, I22 / H22 + "", "") → E22
  126. If(q ≤ 1, Element[L_1, 21]) → I23
  127. If(q ≤ 1, Element[List, 21]) → H23
  128. If(q ≤ 1, Element[L_1, 21] + "", "") → C23
  129. If(q ≤ 1, Element[List, 21] + "", "") → D23
  130. If(q ≤ 1, I23 / H23 + "", "") → E23
  131. Midpoint(C, D) → L
  132. Midpoint(F, E) → N
  133. Intersect(k, i_1) → O
  134. Intersect(l, i_1) → P
  135. Midpoint(O, P) → R
  136. Point(f) → T

AI 绘图提示语参考

画一个函数图像，并展示其导数的几何意义。在函数图像上选择一个点，画出该点的切线，并显示切线的斜率。同时，通过动态变化的点来演示导数的定义和极限概念，包括与x轴的平行线段和垂直线段，以及它们之间的角度关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。