Definition of Derivative - Task 3: From Secant to Tangent

① This example dynamically illustrates how a secant line approaches the tangent line as the increment h tends to zero, visually demonstrating the geometric definition of the derivative. ② The core mathematical concept is the limit definition of the derivative: the derivative at a point equals the limit of the slope of secant lines, involving tangent lines, secant lines, slopes, and the concept of limits. ③ Construction highlights: Uses GeoGebra's Textfield and InputBox for interactive input, If commands for conditional display, Tangent command to draw the tangent line, Line command for the secant, Polygon to construct auxiliary triangles, and sliders (h, n, m) for dynamic parameter changes. Key objects include function f, points A, B, H, and text elements. ④ Suitable for high school and introductory college calculus students to grasp the geometric intuition of derivatives, and useful for teachers as a classroom demonstration or for self-directed exploration.