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Rolle's Theorem

Rolle's Theorem
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2016-02-16 08:22
FunctionCalculusDerivative
In collections Fun with Functions
This example demonstrates a continuous differentiable function over a domain with equal end points. By observing the points where the derivative is zero, the core of Rolle's Theorem is illustrated. The construction uses commands like Polynomial, Root, and Integral in GeoGebra. Suitable for high school mathematics education and learning calculus concepts.

GeoGebra Commands & Parameters

  1. Point(xAxis) → I
  2. Point(xAxis) → H
  3. Polynomial({A, B, C, D, E, F, G}) → f
  4. Min(x(H), x(I)) → xLeft
  5. Root(f(x) - yLeft, Max[x(I), x(H)]) → J
  6. Line(Left, Right) → a
  7. Zip((x(Pnt), f(x(Pnt))), Pnt, list1) → list2
  8. Integral(f, xLeft, xRight) → b