Definition of the Derivative: Secant and Tangent Lines

① This example dynamically shows how a secant line approaches the tangent line, illustrating the derivative as the limit of secant slopes.② Core concepts include the derivative, limits, geometric meaning of secant and tangent lines, and local linearization of function graphs.③ Construction highlights: Line command draws the secant, Tangent command creates the tangent, Textfield and inputBox1 enable interactive parameter entry and live annotations; objects comprise function f, variable a, increment h, points A and B, auxiliary parameters b, c, d, and text labels text1‑text3 for key values.④ Suitable for high‑school calculus introduction to derivatives, university calculus review, or self‑study, helping learners connect geometric intuition with the algebraic definition.