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Application of Derivatives

Application of Derivatives
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2012-04-05 21:18
DerivativeOptimizationGeometric Construction
This example demonstrates how to use derivatives to determine the maximum and minimum values of functions, focusing on core concepts like derivatives and optimization. It constructs geometric models using commands such as Segment, Polygon, Circle, Point, Line, Intersect, OrthogonalLine, Distance, and Perimeter in GeoGebra, making it suitable for high school and above students learning real-world applications of function optimization.

GeoGebra Commands & Parameters

  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