Tangent Lines as Limits of Secant Lines with Sliders

This GeoGebra example dynamically demonstrates how a secant line approaches a tangent line as one point on the curve converges toward another, illustrating the limit definition of the derivative. Core mathematical concepts include limits, differential calculus, secant and tangent slopes, and the geometric interpretation of the derivative as the instantaneous rate of change. The construction uses GeoGebra commands Line and Slope to draw secant and tangent lines and compute their gradients, while Textfield and inputBox1 provide parameter input; objects a, f, a₁, h, A, B, b, and m define the function, variable points, and dynamic line parameters, with a slider controlling h to animate the limiting process. It is suitable for high school calculus introductions, university mathematical analysis courses, and self-study visualizations of derivative fundamentals.