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Curve Discussion: Extremum, Inflection Point

Curve Discussion: Extremum, Inflection Point
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2019-04-25 16:26
FunctionCalculusDerivativeOptimizationGeometric Construction
This example demonstrates curve discussion, focusing on extremum and inflection point. Key mathematical concepts include derivatives, extremum points, and inflection points. Using GeoGebra commands such as Derivative, Point, and Extremum, the example constructs key points of the curve. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Derivative(f) → g'
  2. Point(f') → H
  3. Point(f) → P
  4. Extremum(f) → E_1, E_2
  5. Line(E_1, yAxis) → a
  6. Circle(P, r) → g_1
  7. Tangent(P, f) → e
  8. Intersect(g_1, e, 2) → J
  9. Intersect(g_1, e, 1) → K
  10. Segment(J, K) → Tangente
  11. Slope(e) → i
  12. OrthogonalLine(E_2, xAxis) → b
  13. Derivative(g') → g''
  14. Root(f) → N, N_1, N_2
  15. Line(N, xAxis) → c
  16. Intersect(f, yAxis, 1) → S
  17. OrthogonalLine(S, c) → d
  18. TurningPoint(f) → W_1, W_2, W_3
  19. Line(W_1, d) → j
  20. Line(W_3, d) → l
  21. Intersect(f', a, 1) → E_1'
  22. Intersect(f', b, 1) → E_2'
  23. Intersect(f', d, (0, -10)) → S'
  24. Intersect(f'', j, (-7.071067811865475, -20)) → W_1''
  25. Intersect(f'', l, (7.071067811865475, -20)) → W_3''
  26. Line(W_1'', W_3'') → r_1
  27. Intersect(f'', d, (0, -20)) → W_2''
  28. Line(E_1', E_2') → s
  29. Line(P', P) → h
  30. Intersect(s, h) → A
  31. Tangent(H, f') → c_1
  32. Circle(H, r) → e_1
  33. Intersect(e_1, c_1, 1) → F
  34. Intersect(e_1, c_1, 2) → G
  35. Segment(F, G) → Tangente'
  36. Slope(c_1) → u
  37. Vector(A, P') → w
  38. Segment(A, P) → t
  39. OrthogonalLine(H, s) → a_1
  40. Intersect(r_1, a_1) → B
  41. Intersect(f'', a_1, (-12.555672298084508, -21.62186501006348)) → C
  42. Vector(B, C) → v
  43. Segment(H, B) → b_1
  44. Extremum(f') → D, E, I