Derivative definition via limits: secant lines to tangent slope

This example demonstrates how the derivative is defined using limits by constructing a secant line between two points on a function graph and shrinking the interval until the secant approaches the tangent. It focuses on the core ideas of the derivative as a limit of difference quotients, the geometric meaning of rate of change, and the relationship between secant and tangent lines. In GeoGebra, it is built with commands such as Point (defining points on the graph), Line (drawing the secant), If (updating or selecting configurations depending on parameters), Polygon (highlighting regions or incremental segments), and Tangent (computing the limiting tangent line). Key objects include f (the function), A and B (interval endpoints), Δx and Δy (the geometric increments forming the ratio), and text labels to communicate the definition and the evolving quantities as parameters (e.g., b, n, c, m) change. Suitable for calculus prerequisites, limit-based instruction, and classroom activities that connect algebraic definitions to visual intuition.