导数图像 by Philip Taylor

导数图像 by Philip Taylor
几何画板及绘图内容加载中,请稍等……
2018-07-06 11:48
这个范例展示了导数的图像。它涉及导数这一核心数学概念。通过使用GeoGebra命令如Sequence、Element、Point、Zip、If和NDerivative,可以构造出函数的导数图像。适合高中及以上学生学习导数的概念及其图像表示。

GeoGebra 命令及参数

  1. Sequence(x_1 + (i * w), i, 1, n) → xvals
  2. Element(xvals, A50) → B50
  3. Point(x = B50) → C50
  4. Element(xvals, A49) → B49
  5. Point(x = B49) → C49
  6. Element(xvals, A48) → B48
  7. Point(x = B48) → C48
  8. Element(xvals, A47) → B47
  9. Point(x = B47) → C47
  10. Element(xvals, A46) → B46
  11. Point(x = B46) → C46
  12. Element(xvals, A45) → B45
  13. Point(x = B45) → C45
  14. Element(xvals, A44) → B44
  15. Point(x = B44) → C44
  16. Element(xvals, A43) → B43
  17. Point(x = B43) → C43
  18. Element(xvals, A42) → B42
  19. Point(x = B42) → C42
  20. Element(xvals, A41) → B41
  21. Point(x = B41) → C41
  22. Element(xvals, A40) → B40
  23. Point(x = B40) → C40
  24. Element(xvals, A39) → B39
  25. Point(x = B39) → C39
  26. Element(xvals, A38) → B38
  27. Point(x = B38) → C38
  28. Element(xvals, A37) → B37
  29. Point(x = B37) → C37
  30. Element(xvals, A36) → B36
  31. Point(x = B36) → C36
  32. Element(xvals, A35) → B35
  33. Point(x = B35) → C35
  34. Element(xvals, A34) → B34
  35. Point(x = B34) → C34
  36. Element(xvals, A33) → B33
  37. Point(x = B33) → C33
  38. Element(xvals, A32) → B32
  39. Point(x = B32) → C32
  40. Element(xvals, A31) → B31
  41. Point(x = B31) → C31
  42. Element(xvals, A30) → B30
  43. Point(x = B30) → C30
  44. Element(xvals, A29) → B29
  45. Point(x = B29) → C29
  46. Element(xvals, A28) → B28
  47. Point(x = B28) → C28
  48. Element(xvals, A27) → B27
  49. Point(x = B27) → C27
  50. Element(xvals, A26) → B26
  51. Point(x = B26) → C26
  52. Element(xvals, A25) → B25
  53. Point(x = B25) → C25
  54. Element(xvals, A24) → B24
  55. Point(x = B24) → C24
  56. Element(xvals, A23) → B23
  57. Point(x = B23) → C23
  58. Element(xvals, A22) → B22
  59. Point(x = B22) → C22
  60. Element(xvals, A21) → B21
  61. Point(x = B21) → C21
  62. Element(xvals, A20) → B20
  63. Point(x = B20) → C20
  64. Element(xvals, A19) → B19
  65. Point(x = B19) → C19
  66. Element(xvals, A18) → B18
  67. Point(x = B18) → C18
  68. Element(xvals, A17) → B17
  69. Point(x = B17) → C17
  70. Element(xvals, A16) → B16
  71. Point(x = B16) → C16
  72. Element(xvals, A15) → B15
  73. Point(x = B15) → C15
  74. Element(xvals, A14) → B14
  75. Point(x = B14) → C14
  76. Element(xvals, A13) → B13
  77. Point(x = B13) → C13
  78. Element(xvals, A12) → B12
  79. Point(x = B12) → C12
  80. Element(xvals, A11) → B11
  81. Point(x = B11) → C11
  82. Element(xvals, A10) → B10
  83. Point(x = B10) → C10
  84. Element(xvals, A9) → B9
  85. Point(x = B9) → C9
  86. Element(xvals, A8) → B8
  87. Point(x = B8) → C8
  88. Element(xvals, A7) → B7
  89. Point(x = B7) → C7
  90. Element(xvals, A6) → B6
  91. Point(x = B6) → C6
  92. Element(xvals, A5) → B5
  93. Point(x = B5) → C5
  94. Element(xvals, A4) → B4
  95. Point(x = B4) → C4
  96. Element(xvals, A3) → B3
  97. Point(x = B3) → C3
  98. Element(xvals, A2) → B2
  99. Point(x = B2) → C2
  100. Element(xvals, A1) → B1
  101. Point(x = B1) → C1
  102. Zip(y(A), A, L_2) → usrslopes
  103. Zip((a, f(a)), a, xvals) → points
  104. Zip(x(A) - w2, A, points) → x_{lower}
  105. Zip(x(A) + w2, A, points) → x_{upper}
  106. If(t > 0, Zip[(t * f'(x(A))), A, points], usrslopes) → derivatives
  107. Zip(y(A) + (d * (x(A) - x_1)), A, points, x_1, x_{upper}, d, derivatives) → y_{upper}
  108. Zip(y(A) + (d * (x(A) - x_1)), A, points, x_1, x_{lower}, d, derivatives) → y_{lower}
  109. Zip(Segment[(x_1, y_1), (x_2, y_2)], x_1, x_{lower}, x_2, x_{upper}, y_1, y_{upper}, y_2, y_{lower}) → L_1
  110. Zip((x(A), d), A, points, d, derivatives) → f_{prime}
  111. Zip((x(A), 0), A, points) → xaxispts
  112. Zip(Vector[A, A + (t * (B - A))], A, xaxispts, B, f_{prime}) → vectors
  113. NDerivative(f) →
  114. NDerivative(f) →

AI 绘图提示语参考

画出函数的导数图像,首先生成一系列x值,然后根据这些x值找到对应的函数值,并依次绘制点,最后将这些点用线连接起来,展示函数的导数图像。
以上提示语为根据原始绘图命令整理而来,仅供参考。