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Create a Function: Calculus

Create a Function: Calculus
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2019-08-01 03:27
FunctionCalculusDerivative
This example demonstrates how to create a function based on specific characteristics of its first and second derivatives. It involves core math concepts like calculus, derivatives, real numbers, percentages, tree diagrams, logic, and exponential functions. Constructed using GeoGebra commands such as Min, Max, FitPoly, Sequence, RandomElement, Random, mean, FractionText, CountIf, Sort, Element. Suitable for high school and above, ideal for calculus instruction and formative assessment quiz generation with feedback.

GeoGebra Commands & Parameters

  1. Min({x(A), x(B), x(C)}) → a
  2. Max({x(A), x(B), x(C)}) → b
  3. FitPoly({A, B, C}, 2) → f
  4. Sequence((2 * i), i, -5, 4, 1) → l1
  5. RandomElement(l1) → c
  6. Random(-8, 8) → outputc
  7. Sequence(i, i, c + 2, 10, 2) → l2
  8. RandomElement(l2) → d
  9. mean(c, d) → e
  10. Sequence(i, i, -10, 10, 1) → numlist
  11. FractionText(m) → text1
  12. Random(1, 7) → n
  13. Random(1, 5) → w
  14. Random(1, 2) → p
  15. Random(1, 2) → k
  16. Sequence(c + ((e - c) * i / 50), i, 1, 49, 1) → leftlist
  17. Sequence(e + ((d - e) * i / 50), i, 1, 49, 1) → rightlist
  18. Sequence(g'(Element[leftlist, i]), i, 1, 49, 1) → LeftDs
  19. CountIf(x < 0, LeftDs) → DerivLeftNeg
  20. Sequence(g'(Element[rightlist, i]), i, 1, 49, 1) → RightDs
  21. CountIf(x < 0, RightDs) → DerivRightNeg
  22. Sort({x(A), x(B), x(C)}) → l3
  23. Element(l3, 2) → SecondTest