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Intermediate Value Theorem Demo

Intermediate Value Theorem Demo
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2016-09-16 20:49
FunctionCalculusGeometric Construction
This example demonstrates the Intermediate Value Theorem graphically, showing that a continuous function must take on any intermediate value within a given interval. Key math concepts include continuous functions and the IVT. Construction uses commands like Textfield, CurveCartesian, Line, IntegralBetween with objects such as f, a, b, c. Suitable for high school students and calculus beginners.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox1
  2. CurveCartesian(t, f(t), t, a, b) → c
  3. Line(A, D) → g
  4. Line(B, E) → h
  5. IntegralBetween(((-(x(g) / y(g))) * x) - z(g) / y(g), ((-(x(h) / y(h))) * x) - z(h) / y(h), a, b) → e
  6. Line(A, C) → j
  7. Line(B, F) → k
  8. IntegralBetween(((-(x(g) / y(g))) * x) - z(g) / y(g), ((-(x(h) / y(h))) * x) - z(h) / y(h), -1000000000, 100000000) → d