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Inverse Function and Derivative by Whan Ki Lee

Inverse Function and Derivative by Whan Ki Lee
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2017-02-07 22:24
FunctionCalculusDerivative
This example illustrates the concepts of inverse function and derivative. It shows the geometric meaning of the derivative by drawing a function and its inverse. It uses commands like Function, Point, and Tangent in GeoGebra, suitable for high school math education.

GeoGebra Commands & Parameters

  1. Function((x - 3)^(1 / 3) + 1, -100, 100) → f
  2. Function((x - 1)^(3) + 3, -100, 100) → g
  3. Point(f) → A
  4. Tangent(x(A), f) → a
  5. Tangent(x(B), g) → b

AI Drawing Prompt Reference

Draw the function f(x) = (x - 3)^(1/3) + 1 and its inverse g(x) = (x - 1)^3 + 3, then draw a tangent line at a point on f and another tangent line at the corresponding point on g.
The prompt above was compiled from the original drawing commands and is for reference only.