MathPlotAI Logo MathPlotAI

Verification of Rolle's Theorem

Verification of Rolle's Theorem
Loading the math board and drawing, please wait…
2020-06-03 11:05
FunctionCalculusDerivative
This example demonstrates Rolle's Theorem, which states that if a function f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), and if f(a) = f(b), then there exists at least one point c in (a, b) such that f'(c) = 0. The construction includes the graph of f(x), the graph of f'(x), and the tangent line at x=c, providing a visual representation of the theorem. GeoGebra commands used include Textfield, Derivative, Root, Extremum, Tangent, and Segment. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Textfield(a) → InputBox1
  2. Textfield(b) → InputBox2
  3. Textfield(c) → InputBox3
  4. Textfield(d) → InputBox4
  5. Derivative(f) → f'
  6. Root(f') → B, C
  7. Extremum(f) → D, E
  8. Tangent(D, f) → g
  9. Tangent(E, f) → h
  10. Segment(D, B) → i
  11. Segment(E, C) → j

AI Drawing Prompt Reference

Draw a function graph showing its derivative and two tangent lines, one at the zero of the derivative. The function is continuous on [a, b] and differentiable on (a, b), with f(a) = f(b). Mark the endpoints a and b, the zero of the derivative c, and the extrema of the function. Connect the extrema to the zero of the derivative with line segments to illustrate the relationship between the tangents and the function, visually verifying Rolle's Theorem.
The prompt above was compiled from the original drawing commands and is for reference only.