Investigating the Derivative at a Cusp
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BC Calculus
This example demonstrates the investigation of the derivative at a cusp. The key mathematical concept involved is the derivative. Using GeoGebra commands Tangent and Slope, the function graph at the cusp is constructed. Suitable for high school mathematics education or learning about the concept of derivatives.
GeoGebra Commands & Parameters
Tangent(A, f) → bSlope(b) → m
AI Drawing Prompt Reference
Draw a function graph and add a tangent line at its cusp, then calculate and display the slope of the tangent line to explore the derivative behavior at the cusp. First show the function curve, then add a tangent line at the cusp, and finally label the slope value of the tangent line for observation.
The prompt above was compiled from the original drawing commands and is for reference only.