积极 AI Logo 积极 AI

导数的应用 by sureshbabupp

导数的应用 by sureshbabupp
几何画板及绘图内容加载中，请稍等……
2012-04-05 21:18
导数最值优化几何作图
①本范例演示如何利用导数确定函数的最大和最小值；②涉及核心数学概念：导数、最值优化；③作图要点：使用Segment, Polygon, Circle, Point, Line, Intersect, OrthogonalLine, Distance, Perimeter等GeoGebra命令和对象构建几何模型；④适合高中及以上学生学习和理解实际应用中的函数最值问题。

GeoGebra 命令及参数

  1. Segment(C, D) → a_1
  2. Segment(D, B) → b
  3. Polygon(G, F, E, A) → poly1, g, f, e, a_2
  4. Polygon(J, I, B, H) → poly2, j, i, b_1, h
  5. Polygon(P, N, D, O) → poly3, p, n, d, o
  6. Polygon(K, M, L, C) → poly4, k, m, l, c
  7. Circle(Q, 5 - 2 * a) → q
  8. Point(q) → R
  9. Line(Q, R) → r
  10. Line(R, xAxis) → s
  11. Line(T, r) → t
  12. Intersect(s, t) → U
  13. OrthogonalLine(R, s) → c_1
  14. OrthogonalLine(T, xAxis) → d_1
  15. OrthogonalLine(Q, xAxis) → e_1
  16. OrthogonalLine(U, xAxis) → f_1
  17. Line(S, r) → g_1
  18. Intersect(g_1, c_1) → V
  19. Line(V, s) → h_1
  20. Line(S, xAxis) → i_1
  21. Intersect(i_1, d_1) → W
  22. Line(W, t) → j_1
  23. Intersect(j_1, f_1) → Z
  24. Polygon(S, Q, T, W) → poly5, s_1, q_1, t_1, w
  25. Polygon(V, R, U, Z) → poly6, v, r_1, u, z
  26. Polygon(T, U, Z, W) → poly7, t_2, u_1, z_1, w_1
  27. Polygon(S, Q, R, V) → poly8, s_2, q_2, r_2, v_1
  28. Distance(w, t_2) → k_1
  29. Perimeter(poly7) → l_1
  30. Segment(C, A) → m_1
  31. Segment(A, B) → n_1
  32. Perimeter(poly8) → o_1
  33. Distance(b, n_1) → p_1
  34. Distance(j, h) → b_2
  35. Distance(f, k) → c_2