Derivative Tangent Line Example

This GeoGebra example demonstrates how to construct and visualize the tangent line to a function curve at a movable point, illustrating the geometric meaning of the derivative. The core mathematical concept is that the slope of the tangent line equals the derivative value of the function at the point of tangency. The construction uses GeoGebra commands such as Point to create a dynamic point A on the function f, Line to draw a line through A, Tangent to generate the tangent line directly, and Segment to restrict the tangent to a visible segment. Additional objects like B, C, D, E, F are used to mark points or segments for clarity. This example is suitable for high school or introductory college calculus students to explore the relationship between derivatives and tangent slopes, and can be used for classroom demonstrations or self-study.