Derivative Definition: Secant Approximating Tangent Dynamic Demo

This example demonstrates the definition of derivative at a point on a function through interactive operation. Move the red point A to change the point of interest, adjust the slider h to change the increment of x, and observe how the slope of secant line AB approaches the slope of tangent line as h approaches zero, intuitively understanding derivative as the limit concept. Construction: Use GeoGebra commands Point, Line, Textfield to create function f, point A, variable h, inputBox1 and text1, generating an adjustable secant AB and dynamically changing h via slider or input box. Suitable for high school math students or college calculus beginners, to intuitively understand derivative concept, limit idea, and the relationship between secant and tangent, also as a classroom teaching demonstration tool.