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First Derivative Test

First Derivative Test
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2015-08-10 21:42
FunctionCalculusDerivativeGraphing
This example demonstrates the application of the first derivative test in identifying extrema of a function; involves core math concepts like derivatives, function monotonicity, and extremum determination; constructed using GeoGebra commands/objects such as Intersect, Tangent, Point, Derivative, Line to build function graphs, derivative graphs, and extrema points; suitable for high school and above students learning calculus and extremum determination methods.

GeoGebra Commands & Parameters

  1. Intersect(f, d, 1) → C
  2. Tangent(C, f) → a
  3. Intersect(f, n, 1) → E
  4. Tangent(E, f) → b
  5. Point(f) → F
  6. Point(f) → G
  7. Point(f) → H
  8. Point(f) → I
  9. Point(f) → J
  10. Point(f) → L
  11. Point(f) → M
  12. Point(f) → N
  13. Point(f) → O
  14. Derivative(f) → f'
  15. Point(f') → U
  16. Line(U, F) → e
  17. Point(f') → V
  18. Point(f') → W
  19. Point(f') → Z
  20. Point(f') → A_1
  21. Point(f') → C_1
  22. Point(f') → D_1
  23. Point(f') → E_1
  24. Point(f') → F_1
  25. Intersect(f', c, 1) → K
  26. Intersect(f, c, 1) → B_1
  27. Intersect(f', g, 1) → Q
  28. Intersect(f', d, 1) → R
  29. Intersect(f, g, 1) → B
  30. Intersect(f, l, 1) → A
  31. Intersect(f', l, 1) → P
  32. Intersect(f', n, 1) → S
  33. Intersect(f, p, 1) → D
  34. Intersect(f', p, 1) → T

AI Drawing Prompt Reference

Draw a function and its derivative, marking extrema and derivative zeros, connect extrema with tangents and zeros with lines to show function monotonicity and extremum determination.
The prompt above was compiled from the original drawing commands and is for reference only.