Derivative and Tangent Line: Dynamic Slope Exploration

This GeoGebra example demonstrates the geometric meaning of the derivative by dynamically showing how the slope of a tangent line to a function graph corresponds to the derivative value at a point. Core mathematical concepts include derivatives, tangent lines, slope, functions, and the relationship between a function and its derivative graph. The construction uses GeoGebra commands such as Point, Tangent, Slope, and Derivative, with objects including a, b, c, d, e, f, A, g, m, D, f′, h, and i to build the function curve, tangent point, tangent line, and slope indicator. It is suitable for high school calculus introductions and undergraduate mathematics analysis courses, ideal for classroom demonstrations and independent inquiry into the geometric interpretation of derivatives.