H - Derivatives: Tangent, Slope, and Histogram Visualization

① This example demonstrates the geometric meaning of derivatives by showing the tangent line and its slope at a moving point on a function graph, alongside a histogram for data distribution. ② Core mathematical concepts include the derivative as the instantaneous rate of change, the slope of the tangent line, and connections to linear programming/optimization and real numbers. ③ Construction uses GeoGebra commands: Point, Tangent, Slope, and Segment, with objects f (function), A (point), g (tangent), m (slope), S and h (segments), allowing dynamic exploration as point A moves along the curve. ④ Suitable for high school to early college calculus courses, ideal for teachers demonstrating derivative concepts and local linear approximation, or for students to investigate relationships between derivatives, monotonicity, and extrema.