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Try to Graph the Derivative Function

Try to Graph the Derivative Function
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2018-07-18 05:44
FunctionCalculusDerivative
This example demonstrates how to graph the derivative function based on the given function graph. Key mathematical concepts include derivatives. Using GeoGebra commands such as Sequence, Function, and Segment, the derivative function graph can be constructed. Suitable for high school mathematics education and learning calculus concepts.

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

AI Drawing Prompt Reference

Draw a function graph and its derivative graph. First, generate a random function graph. Then, based on this graph, create a derivative function graph. Next, draw a series of vertical segments, with each segment's length representing the function value and its position corresponding to integer points on the x-axis. Finally, fit polynomials to connect the vertices of adjacent segments, approximating the derivative function's curve.
The prompt above was compiled from the original drawing commands and is for reference only.