Derivative of x^2: Visualizing the Tangent Slope on a Parabola

① This GeoGebra example dynamically illustrates the definition of the derivative as the slope of the tangent line using the parabola y = x², showing how the secant line's slope approaches the tangent slope as two points converge. ② Core mathematical concepts include the limit definition of the derivative, tangent and secant lines, slope, rate of change, and continuity, providing a foundational visual for differential calculus. ③ Construction details: The applet uses Textfield for inputting the function, Point and Segment to create points and the secant chord, Line for the tangent, and Vector to display slope components; Sliders control the parameter h, while buttons (clearButton, upButton, downButton, etc.) reset or adjust the view, enabling interactive exploration. ④ Suitable for high school and early college students learning calculus, this tool serves as an effective classroom demonstration or self-paced exploration to grasp the geometric meaning of derivatives.