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导数构建器

导数构建器
几何画板及绘图内容加载中，请稍等……
2016-06-28 22:29
解析几何微积分几何作图
①本范例演示如何通过动态构建点、线段和文本字段来可视化导数的概念；②涉及的核心数学概念包括导数、坐标几何、算术运算和三角形；③作图要点提炼自构造摘要，使用了Corner、Point、If、Segment、Textfield等GeoGebra命令和对象；④适合高中及以上学生学习和理解微积分中的导数计算与几何意义。

GeoGebra 命令及参数

  1. Corner(3) → c3
  2. Corner(1) → c1
  3. Point(x = B2) → C2
  4. Point(x = B3) → C3
  5. Point(x = B4) → C4
  6. Point(x = B5) → C5
  7. Point(x = B6) → C6
  8. Point(x = B7) → C7
  9. Point(x = B8) → C8
  10. Point(x = B9) → C9
  11. Point(x = B10) → C10
  12. Point(x = B11) → C11
  13. Point(x = B12) → C12
  14. Point(x = B13) → C13
  15. Point(x = B14) → C14
  16. Point(x = B15) → C15
  17. Point(x = B16) → C16
  18. Point(x = B17) → C17
  19. Point(x = B18) → C18
  20. Point(x = B19) → C19
  21. Point(x = B20) → C20
  22. If(togfp ≟ 0, "Show f'(x)", "Hide f'(x)") → ShowHidefprime
  23. Segment(D2 + ((h * delx / 2) * (1, y(C2))), D2 - ((h * delx / 2) * (1, y(C2)))) → E2
  24. Segment(D3 + ((h * delx / 2) * (1, y(C3))), D3 - ((h * delx / 2) * (1, y(C3)))) → E3
  25. Textfield(f) → InputfOFx
  26. Segment(D4 + ((h * delx / 2) * (1, y(C4))), D4 - ((h * delx / 2) * (1, y(C4)))) → E4
  27. Segment(D5 + ((h * delx / 2) * (1, y(C5))), D5 - ((h * delx / 2) * (1, y(C5)))) → E5
  28. Segment(D6 + ((h * delx / 2) * (1, y(C6))), D6 - ((h * delx / 2) * (1, y(C6)))) → E6
  29. Segment(D7 + ((h * delx / 2) * (1, y(C7))), D7 - ((h * delx / 2) * (1, y(C7)))) → E7
  30. Segment(D8 + ((h * delx / 2) * (1, y(C8))), D8 - ((h * delx / 2) * (1, y(C8)))) → E8
  31. Segment(D9 + ((h * delx / 2) * (1, y(C9))), D9 - ((h * delx / 2) * (1, y(C9)))) → E9
  32. Segment(D10 + ((h * delx / 2) * (1, y(C10))), D10 - ((h * delx / 2) * (1, y(C10)))) → E10
  33. Segment(D11 + ((h * delx / 2) * (1, y(C11))), D11 - ((h * delx / 2) * (1, y(C11)))) → E11
  34. Segment(D12 + ((h * delx / 2) * (1, y(C12))), D12 - ((h * delx / 2) * (1, y(C12)))) → E12
  35. Segment(D13 + ((h * delx / 2) * (1, y(C13))), D13 - ((h * delx / 2) * (1, y(C13)))) → E13
  36. Segment(D14 + ((h * delx / 2) * (1, y(C14))), D14 - ((h * delx / 2) * (1, y(C14)))) → E14
  37. Segment(D15 + ((h * delx / 2) * (1, y(C15))), D15 - ((h * delx / 2) * (1, y(C15)))) → E15
  38. Segment(D16 + ((h * delx / 2) * (1, y(C16))), D16 - ((h * delx / 2) * (1, y(C16)))) → E16
  39. Segment(D17 + ((h * delx / 2) * (1, y(C17))), D17 - ((h * delx / 2) * (1, y(C17)))) → E17
  40. Segment(D18 + ((h * delx / 2) * (1, y(C18))), D18 - ((h * delx / 2) * (1, y(C18)))) → E18
  41. Segment(D19 + ((h * delx / 2) * (1, y(C19))), D19 - ((h * delx / 2) * (1, y(C19)))) → E19
  42. Segment(D20 + ((h * delx / 2) * (1, y(C20))), D20 - ((h * delx / 2) * (1, y(C20)))) → E20
  43. Point(x = B1) → C1
  44. Segment(D1 + ((h * delx / 2) * (1, y(C1))), D1 - ((h * delx / 2) * (1, y(C1)))) → E1
  45. Textfield(g) → InputGuess

AI 绘图提示语参考

绘制一个动态导数演示图：在坐标平面上，先放置一个可编辑的函数输入框和猜测输入框，并显示一个切换按钮用于显示或隐藏导函数曲线。在函数曲线上等间距取一系列点，从每个点出发，沿水平方向绘制一条短线段，线段长度由参数控制，代表该点处的微分增量。同时，在图形角落标注坐标参考点。整体布局应清晰展示函数曲线、采样点及其对应的水平切线片段，便于观察导数随位置的变化。
以上提示语为根据原始绘图命令整理而来，仅供参考。