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Dynamic Definition of a Derivative

Dynamic Definition of a Derivative
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2015-09-21 20:42
FunctionCalculusDerivativeGeometric Construction
This example dynamically demonstrates the definition of the derivative for the function f(x)=(x^2)/5, visually showing how the slope of a secant line approaches the slope of a tangent line as points A and B move closer. Core math concepts include derivative, secant line, tangent line, and limit. Constructed using GeoGebra commands like Function, Point, Line, Segment, and objects such as f, A, B, C, etc., with sliders for dynamic visualization. Suitable for high school students and above learning calculus, or for educational demonstrations.

GeoGebra Commands & Parameters

  1. Function((1 / 5 * x^(2)), -5, 5) → f
  2. Point(f) → A
  3. Point(f) → B
  4. Line(A, B) → a
  5. Segment(B, C) → b
  6. Segment(A, C) → c

AI Drawing Prompt Reference

Draw a function graph and dynamically show two points on it. As these points move closer, draw the secant line connecting them and the tangent line passing through one of the points, illustrating how the slope of the secant line approaches the slope of the tangent line, demonstrating the definition of a derivative.
The prompt above was compiled from the original drawing commands and is for reference only.