Relationship Between Function and First Derivative

This example demonstrates the relationship between a function's graph and its first derivative, visually illustrating the geometric and physical meanings of derivatives. Core mathematical concepts include the definition of derivatives, the monotonicity and concavity of functions, as well as inflection points. The construction uses GeoGebra commands and objects like Textfield, Point, Tangent, and Slope to dynamically interact and show the changing trends of the function in different intervals. Suitable for high school and above learning calculus and function analysis, helping to understand the application of derivatives in function research.