Dynamic Derivative 3: Tangent Slope Interacting with Triangle Geometry

This interactive GeoGebra example dynamically illustrates the relationship between the slope of a tangent line (the derivative) at a point on a function graph and associated triangle geometry elements. Core mathematical concepts include the geometric meaning of derivatives, tangent slope, orthocenter, incircle, isosceles triangles, and straight lines. Construction highlights: using GeoGebra commands Point, Line, Tangent, and Slope; objects include function f, tangent line h, moving point X, lines b, d, e, a, g, points C and D, and multiple text labels (text1 to text5) that together form a dynamic figure featuring an orthocenter, incircle, and isosceles triangle structure. Suitable for high school or early college students to grasp the connection between calculus and geometry, and for teachers as an interactive demonstration tool.