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Slope, Average Rate, and Instantaneous Rate of Change

Slope, Average Rate, and Instantaneous Rate of Change
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2014-02-04 16:57
FunctionCalculusDerivative
This applet demonstrates the concept of slope for both straight lines and the tangent at a point on a curve. It also shows how to calculate average and instantaneous rates. Using GeoGebra commands like Point, Tangent, Line, etc., you can dynamically explore these concepts. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(c) → P
  2. Tangent(P, c) → a,
  3. Point(c) → Q
  4. Line(P, Q) → b
  5. Point(c) → A
  6. Line(P, A) → d
  7. Point(c) → B
  8. Line(P, B) → e
  9. Point(c) → C
  10. Tangent(C, c) → f,
  11. Vector(P, (x(Q), y(P))) → u
  12. Vector((x(Q), y(P)), Q) → v
  13. Line(P, Q) → j
  14. Point(j) → Q'
  15. Vector((x(Q'), y(P)), Q') → w
  16. Vector(P, (x(Q'), y(P))) → z
  17. Point(j) → C'
  18. Segment(C', D') → l
  19. OrthogonalLine(D', l) → m
  20. Intersect(m, j) → E
  21. Polygon(C', D', E) → poly1, e_1, c', d_1
  22. Intersect(n, f) → F
  23. Polygon(C, D, F) → poly2, f_1, c_1, d_2
  24. Intersect(p, a) → G
  25. Polygon(P, P_x, G) → poly3, g_1, p_1, p_x

AI Drawing Prompt Reference

Draw a straight line and a curve, then select a point on the curve to draw a tangent line, showing the relationship between the tangent and the line. Select two points on the line, connect them, and draw a parallel line to this segment. On the curve, select three more points, draw tangents at these points, and show their relationships with the curve. Finally, connect the intersection points of the tangents with the curve to form multiple polygons, visually demonstrating the concepts of slope, average rate of change, and instantaneous rate of change.
The prompt above was compiled from the original drawing commands and is for reference only.