Dynamic Visualization of Derivative Definition: From Secant to Tangent Limit

① This example dynamically demonstrates the geometric essence of the derivative definition: as a moving point B approaches a fixed point A along a function curve, the secant line AB gradually converges to the tangent line, visually showing that the derivative is the slope of the tangent. ② Core mathematical concepts include the limit definition of the derivative, secant slope, tangent slope, special points on a function graph, and geometric relations in 3D vector space. ③ Construction highlights: using GeoGebra commands such as Point (creating points A, B, etc.), If (conditional logic), Line (constructing secants), Segment (drawing segments), Translate (shifting objects), Textfield (input boxes), along with buttons (button1, button2) and sliders (step, SPEED) to control animation speed and step size; objects include function f, point H, line l, segments a, b, etc., with dynamic adjustment of h to transition from secant to tangent. ④ Suitable for high school to early college calculus courses, helping students intuitively grasp the derivative definition, and serving as an interactive tool for classroom demonstrations or self-directed exploration.