Geometric Demo of Function Tangent, Normal, and Derivative

This example selects a point on a function graph and constructs the tangent line and the normal line, highlighting how their geometric relationship reflects the derivative at that point. It focuses on the definition of a tangent, the fact that the normal is perpendicular to the tangent, and the key interpretation of the derivative as the slope of the tangent line. The construction uses GeoGebra commands Tangent to create the tangent at the chosen point, OrthogonalLine to build the normal as the line perpendicular to the tangent, Segment to connect relevant points/segments for clarity, and Angle to visualize the angle information that supports the orthogonality idea. The main objects include the function f, the selected point/parameters (such as a and t), the tangent (t) and the normal (g), together with text labels (text1–text6, text2–text5) to annotate angles and derivative-related meaning. Suitable for advanced high school learners and the beginning of calculus courses, as well as classroom demonstrations and conceptual practice.