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Graphs of First Derivatives

Graphs of First Derivatives
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2018-09-27 07:33
FunctionCalculusDerivativeGraphing
This example demonstrates the relationship between the graph of a function and its first derivative, including tangents and monotonicity. It uses GeoGebra commands like Textfield, Derivative, Tangent, InputBox, sliders, and buttons to interactive explore key calculus concepts. Suitable for high school and above students learning derivatives and their applications.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox1
  2. Derivative(f, x) → b
  3. Tangent(a, f) → g

AI Drawing Prompt Reference

Draw the graph of a function and its first derivative, also include a tangent line on the function graph to show the point of tangency, allow interactive input to change the function's expression, visually demonstrating the relationship between the function and its derivative, and how the tangent line reflects the monotonicity changes of the function.
The prompt above was compiled from the original drawing commands and is for reference only.