Definition of Derivative: Secant Slope Approaching Tangent Slope by user779

① This example visually demonstrates the definition of the derivative: as the increment h approaches zero, the slope of the secant line through two points on a function graph approaches the slope of the tangent line at the point, revealing the geometric meaning of the derivative. ② Core mathematical concepts include the derivative definition, limits, secant and tangent lines, slope, function graphs, and the Pythagorean theorem (used to construct auxiliary right triangles for geometric insight). ③ Construction details: using GeoGebra commands Point, Segment, Line, OrthogonalLine, Intersect, Angle, Tangent, If, and LaTeX, the construction builds function f, moving point A, increment h, secant-related points B_1 and B, perpendicular intersection C, tangent line g, and auxiliary objects such as triangles, vectors, angle α, and text labels (testo1–testo5). A slider controls h to animate the transition from secant to tangent. ④ Suitable for high school and early college students learning calculus, this interactive tool helps understand the intuitive background of the derivative and can be used for classroom demonstrations or independent exploration.