Mean Value Theorem

Mean Value Theorem
Loading the math board and drawing, please wait…
2016-05-17 02:32
This example demonstrates the Mean Value Theorem by dragging a point along a curve. The Mean Value Theorem is a fundamental concept in calculus, stating that for a continuous function on a closed interval, there exists at least one point where the derivative equals the average rate of change over the interval. Using commands like Segment, Point, Tangent, Slope, Line, and Textfield in GeoGebra, this example helps to understand the core idea of the Mean Value Theorem. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment((a, f(a)), (b, f(b))) → c
  2. Point(f) → A
  3. Tangent(A, f) → d
  4. Slope(d) → d_slope
  5. Line((b, f(b)), (a, f(a))) → e
  6. Textfield(g) → InputBox1
  7. Segment((a, 0), (a, f(a))) → h
  8. Segment((b, 0), (b, f(b))) → i
  9. Textfield(a) → InputBox2
  10. Textfield(b) → InputBox3