积极 AI Logo 积极 AI

曲线讨论：极值、拐点

曲线讨论：极值、拐点
几何画板及绘图内容加载中，请稍等……
2019-04-25 16:26
函数微积分导数最值优化几何作图
本范例演示了曲线讨论中的极值、拐点等内容。涉及的核心数学概念包括导数、极值点、拐点等。通过使用GeoGebra命令如Derivative、Point、Extremum等，可以构造出曲线的导数、极值点、拐点等关键点。适合高中数学教学和学习使用。

GeoGebra 命令及参数

  1. Derivative(f) → g'
  2. Point(f') → H
  3. Point(f) → P
  4. Extremum(f) → E_1, E_2
  5. Line(E_1, yAxis) → a
  6. Circle(P, r) → g_1
  7. Tangent(P, f) → e
  8. Intersect(g_1, e, 2) → J
  9. Intersect(g_1, e, 1) → K
  10. Segment(J, K) → Tangente
  11. Slope(e) → i
  12. OrthogonalLine(E_2, xAxis) → b
  13. Derivative(g') → g''
  14. Root(f) → N, N_1, N_2
  15. Line(N, xAxis) → c
  16. Intersect(f, yAxis, 1) → S
  17. OrthogonalLine(S, c) → d
  18. TurningPoint(f) → W_1, W_2, W_3
  19. Line(W_1, d) → j
  20. Line(W_3, d) → l
  21. Intersect(f', a, 1) → E_1'
  22. Intersect(f', b, 1) → E_2'
  23. Intersect(f', d, (0, -10)) → S'
  24. Intersect(f'', j, (-7.071067811865475, -20)) → W_1''
  25. Intersect(f'', l, (7.071067811865475, -20)) → W_3''
  26. Line(W_1'', W_3'') → r_1
  27. Intersect(f'', d, (0, -20)) → W_2''
  28. Line(E_1', E_2') → s
  29. Line(P', P) → h
  30. Intersect(s, h) → A
  31. Tangent(H, f') → c_1
  32. Circle(H, r) → e_1
  33. Intersect(e_1, c_1, 1) → F
  34. Intersect(e_1, c_1, 2) → G
  35. Segment(F, G) → Tangente'
  36. Slope(c_1) → u
  37. Vector(A, P') → w
  38. Segment(A, P) → t
  39. OrthogonalLine(H, s) → a_1
  40. Intersect(r_1, a_1) → B
  41. Intersect(f'', a_1, (-12.555672298084508, -21.62186501006348)) → C
  42. Vector(B, C) → v
  43. Segment(H, B) → b_1
  44. Extremum(f') → D, E, I