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Derivative Definition at a Cusp

Derivative Definition at a Cusp
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2018-10-10 10:18
FunctionCalculusDerivativeLimitGeometric Construction
This example demonstrates the derivative definition at a cusp. Key mathematical concepts include derivatives and limits. Using GeoGebra commands such as Vector, Textfield, Tangent, and Line, the function graph at the cusp is constructed. Suitable for high school mathematics education and learning derivative concepts.

GeoGebra Commands & Parameters

  1. Vector(A, (x(B), y(A))) → u
  2. Vector((x(B), y(A)), B) → v
  3. Textfield(f) → InputBox1
  4. Textfield(a) → InputBox2
  5. Tangent(A, f) → i
  6. Line(A, B) → g

AI Drawing Prompt Reference

Draw a function graph with a cusp at points A and B, and a tangent line i at point A. Use vectors u and v to represent the vectors from A to B and from B to A. Input the function expression f and constant a via text boxes. Draw a line g passing through points A and B, and add text to describe the concepts of derivatives and limits.
The prompt above was compiled from the original drawing commands and is for reference only.