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Graphical Animation of Average Value

Graphical Animation of Average Value
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2014-11-20 13:55
FunctionCalculusGraphing
In collections Average Value
This example demonstrates the graphical animation of the average y-value of a function over an interval. It involves core calculus concepts like integration, function graphs, and average value over a range. Constructed using GeoGebra commands such as Function, Integral, and Segment, along with objects like segments and text. Ideal for high school and above students to visualize and understand the concept of average value in functions, useful for calculus instruction.

GeoGebra Commands & Parameters

  1. Function((-x^(2)) + (5 * x), 0, 4) → f
  2. Integral(f, 0, 4) → b
  3. Function(b / 4, 0, 4) → g
  4. Function((a * g(x)) + ((1 - a) * f(x)), 0, 4) → h
  5. Integral(h, 0, 4) → Area
  6. Segment(V, A) → c
  7. Segment(W, B) → d
  8. Segment(Z, C) → e
  9. Segment(A_1, D) → i
  10. Segment(B_1, E) → j
  11. Segment(C_1, F) → k
  12. Segment(G, D_1) → l
  13. Segment(H, E_1) → m
  14. Segment(I, F_1) → n
  15. Segment(J, G_1) → p
  16. Segment(K, H_1) → q
  17. Segment(L, I_1) → r
  18. Segment(M, J_1) → s
  19. Segment(N, K_1) → t
  20. Segment(O, L_1) → a_1
  21. Segment(P, M_1) → b_1
  22. Segment(Q, N_1) → c_1
  23. Segment(R, O_1) → d_1
  24. Segment(S, P_1) → e_1
  25. Segment(Q_1, T) → f_1
  26. Segment(R_1, U) → g_1