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Incremental Ratio Demonstration

Incremental Ratio Demonstration
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2017-10-29 01:50
Coordinate GeometryCalculusDerivativeGeometric Construction
This example demonstrates the geometric representation of the incremental ratio between two points on a function graph. It involves core mathematical concepts such as derivatives, upper and lower sums (Riemann sums), difference and slope, unit circle, intersections, and confidence intervals. The construction utilizes GeoGebra commands like Intersect, OrthogonalLine, Segment, Vector, Angle, and If. It is suitable for high school and above students studying calculus and analytical geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. OrthogonalLine(A, yAxis) → g
  3. OrthogonalLine(B, yAxis) → h_1
  4. OrthogonalLine(B, xAxis) → i
  5. OrthogonalLine(A, xAxis) → j
  6. Intersect(j, xAxis) → C
  7. Intersect(i, xAxis) → C_1
  8. Intersect(h_1, yAxis) → E
  9. Intersect(g, yAxis) → F
  10. Intersect(i, g) → H
  11. Segment(C, C_1) → h_2
  12. Segment(A, H) → k
  13. Segment(H, B) → l
  14. Segment(A, F) → m
  15. Segment(B, E) → n
  16. Vector(C_1, C) → u
  17. Vector(C, C_1) → v
  18. Vector(B, H) → w
  19. Vector(H, B) → b
  20. Vector(A, H) → c
  21. Vector(H, A) → d
  22. Segment(C, A) → q
  23. Segment(C_1, H) → r
  24. Angle(H, A, B) → α
  25. Intersect(t, r) → I
  26. Intersect(t, i) → D
  27. Angle(H, A, D) → β
  28. Segment(A, B) → f
  29. If(x(A) ≟ x(B), (p'(x(A)) * (x - x(A))) + y(A), ((y(B) - y(A)) / (x(B) - x(A)) * (x - x(A))) + y(A)) → r_{AB}
  30. Vector(H, H1) → hh1
  31. Vector(D, D1) → dd1
  32. Vector(H1, D1) → dyup
  33. Vector(D1, H1) → dydw