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Derivative Definition Demo

Derivative Definition Demo
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2013-09-25 20:46
FunctionCoordinate GeometryCalculusDerivativeLimit
In collections BC Calculus
This example dynamically illustrates the definition of a derivative, showing the instantaneous rate of change of a function at a point. Core math concepts include functions, limits, slopes, and linear approximations. It is constructed using GeoGebra commands like Line, Segment, Textfield, and Slope, with objects such as a, f, A, h, B, etc. Suitable for high school students and above learning calculus basics, or for teacher demonstrations.

GeoGebra Commands & Parameters

  1. Line(A, B) → c
  2. Segment(A, (x(A), 0)) → g
  3. Textfield(f) → inputBox1
  4. Segment(B, C) → b
  5. Slope(c) → m

AI Drawing Prompt Reference

Draw a function with a dynamically illustrated derivative definition, showing a point, the tangent line at that point, and a perpendicular line from the point to the x-axis, including the foot of the perpendicular and a secant line through the foot approaching the tangent line, with a text box for inputting the function expression to dynamically adjust the secant slope until it approximates the tangent slope, demonstrating the instantaneous rate of change.
The prompt above was compiled from the original drawing commands and is for reference only.