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Derivative as a Function

Derivative as a Function
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2019-02-24 18:51
FunctionCalculusDerivative
This example illustrates the concept of the derivative as a function. By plotting the graph of a function, users can observe how the derivative function reflects the slope changes of the original function. Commands like Point, OrthogonalLine, Tangent, and Slope are used to help users understand the geometric meaning of the derivative.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. OrthogonalLine(A, xAxis) → i
  3. Tangent(A, f) → g
  4. Slope(g) → m

AI Drawing Prompt Reference

Draw a function f(x), then select a point A on the function, draw the tangent line g at point A, calculate the slope m of the tangent line, and draw a line i that is perpendicular to the tangent line. Observe how the slope m changes as point A moves along the function f(x).
The prompt above was compiled from the original drawing commands and is for reference only.