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Graph the Derivative Function

Graph the Derivative Function
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2019-01-12 00:42
FunctionCalculusDerivativeGraphing
This example demonstrates how to graph the derivative function of a given function, involving core math concepts like derivatives, function graphs, and rates of change. Key GeoGebra commands used include Sequence, Corner, FitPoly, Function, Segment, and Point for constructing the graph, suitable for high school calculus students or teachers.

GeoGebra Commands & Parameters

  1. Sequence((i, Random[-2, 3] + (0 * dummy)), i, -12, 12, 3) → fPointList
  2. Corner(1) → panelPt1
  3. Corner(4) → panelPt4
  4. FitPoly(fPointList, Length[fPointList] - 1) → f
  5. Function(f, -6, 6) → fRes
  6. Function(g, -6, 6) → gRes
  7. Segment((-6, -3.5), (-6, 4.5)) → segA
  8. Segment((-5, -3.5), (-5, 4.5)) → segB
  9. Segment((-4, -3.5), (-4, 4.5)) → segC
  10. Segment((-3, -3.5), (-3, 4.5)) → segD
  11. Segment((-2, -3.5), (-2, 4.5)) → segE
  12. Segment((-1, -3.5), (-1, 4.5)) → segF
  13. Segment((0, -3.5), (0, 4.5)) → segG
  14. Segment((1, -3.5), (1, 4.5)) → segH
  15. Segment((2, -3.5), (2, 4.5)) → segI
  16. Segment((3, -3.5), (3, 4.5)) → segJ
  17. Segment((4, -3.5), (4, 4.5)) → segK
  18. Segment((5, -3.5), (5, 4.5)) → segL
  19. Segment((6, -3.5), (6, 4.5)) → segM
  20. Point(segA) → A
  21. Point(segB) → B
  22. Point(segC) → C
  23. Point(segD) → D
  24. Point(segE) → E
  25. Point(segF) → F
  26. Point(segG) → G
  27. Point(segH) → H
  28. Point(segI) → I
  29. Point(segJ) → J
  30. Point(segK) → K
  31. Point(segL) → L
  32. Point(segM) → M
  33. FitPoly({A, B, C}, 2) → parABC
  34. FitPoly({C, D, E}, 2) → parCDE
  35. FitPoly({E, F, G}, 2) → parEFG
  36. FitPoly({G, H, I}, 2) → parGHI
  37. FitPoly({I, J, K}, 2) → parIJK
  38. FitPoly({K, L, M}, 2) → parKLM
  39. FitPoly({B, C, D}, 2) → parBCD
  40. FitPoly({D, E, F}, 2) → parDEF
  41. FitPoly({F, G, H}, 2) → parFGH
  42. FitPoly({H, I, J}, 2) → parHIJ
  43. FitPoly({J, K, L}, 2) → parJKL
  44. Function(parABC, x(A), x(B)) → conAB
  45. Function((parABC(x) * (1 - (x + 5))) + (parBCD(x) * (x + 5)), -5, -4) → conBC
  46. Function((parBCD(x) * (1 - (x + 4))) + (parCDE(x) * (x + 4)), -4, -3) → conCD
  47. Function((parCDE(x) * (1 - (x + 3))) + (parDEF(x) * (x + 3)), -3, -2) → conDE
  48. Function((parDEF(x) * (1 - (x + 2))) + (parEFG(x) * (x + 2)), -2, -1) → conEF
  49. Function((parEFG(x) * (1 - (x + 1))) + (parFGH(x) * (x + 1)), -1, 0) → conFG
  50. Function((parFGH(x) * (1 - (x + 0))) + (parGHI(x) * (x + 0)), 0, 1) → conGH
  51. Function((parGHI(x) * (1 - (x - 1))) + (parHIJ(x) * (x - 1)), 1, 2) → conHI
  52. Function((parHIJ(x) * (1 - (x - 2))) + (parIJK(x) * (x - 2)), 2, 3) → conIJ
  53. Function((parIJK(x) * (1 - (x - 3))) + (parJKL(x) * (x - 3)), 3, 4) → conJK
  54. Function((parJKL(x) * (1 - (x - 4))) + (parKLM(x) * (x - 4)), 4, 5) → conKL
  55. Function(parKLM, 5, 6) → conLM
  56. Segment(Q, P) → h

AI Drawing Prompt Reference

Draw the graph of a function and its derivative. First, generate a series of random points and fit them to a polynomial function to plot the function. Then, place multiple horizontal line segments at equal intervals on the x-axis and place a point on each segment. Finally, fit quadratic polynomials to these points and connect them with smooth curves to obtain the derivative graph.
The prompt above was compiled from the original drawing commands and is for reference only.