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Fundamental Theorem of Calculus (Derivative)

Fundamental Theorem of Calculus (Derivative)
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2018-07-21 06:04
FunctionCalculusDerivativeIntegralLimit
In collections Mapping Diagrams: From AB to C&DE, Resource
This example illustrates the derivative part of the Fundamental Theorem of Calculus. It helps students understand the relationship between derivatives and integrals by constructing the connection between them. Commands used include Segment, Point, Integral, Extremum, Intersect, Textfield, Max, Min, Vector, Line, etc. Suitable for high school calculus courses.

GeoGebra Commands & Parameters

  1. Segment(x_a, x_b) → intab
  2. Point(intab) → x_c
  3. Integral(P, a, y(x_c)) → Intgrl
  4. Integral(P, y(x_c), y(x_c) + h) → Intgrl1
  5. Extremum(P, a, b) → M,
  6. Intersect(P1, e, (1.2583057391813939, 2.5833333333333335)) → C
  7. Textfield(P) → inputBox1
  8. Textfield(a) → inputBox2
  9. Textfield(b) → inputBox3
  10. Max({y(M), P(a), P(b)}) → MAX
  11. Min({y(M), P(a), P(b)}) → MIN
  12. Vector(Max_{f}, S_2) → u
  13. Vector(Min_{f}, T_1) → v
  14. Vector(z_*, U_2) → w
  15. Line(U_2, z_*) → i
  16. Line(T_1, Min_{f}) → j
  17. Vector(C_*, z_*) → z
  18. Integral(MAX, a, b) → MaxRec
  19. Integral(MIN, a, b) → MinRec
  20. Integral(Intgrl1 / h, y(x_c), y(x_c) + h) → mvt
  21. Vector(x_c, Pc) → k
  22. Integral(P, a, b) → Intgrlab
  23. Integral(P, a, y(x_c) + h) → Intgrlach
  24. Segment(PIac, P0) → r
  25. Vector(PIac, PIach) → u_1
  26. Vector(P0, U_2) → v_1
  27. Vector(P0, DSdt) → l
  28. Vector(P0, Pc1) → s