Estimating Rate of Change: Geometric Intuition of Derivatives

This example demonstrates how to estimate the rate of change of a function using tangent lines through dynamic geometry. ①What it shows: Based on an adjustable function graph, it illustrates the process of secants approaching tangents, presenting the geometric meaning of derivatives; ②Core math concepts: derivative definition, rate of change, tangent slope, limit concept; ③Construction: Uses Point command to create movable points A and B, Tangent for tangent lines, Line for secants, Intersect to find intersections, Segment to measure lengths, Distance to calculate distances, If for conditional logic, Midpoint to find midpoints, InputBox1 for parameter input; ④Suitable for high school or early college calculus introduction,可以作为导数概念教学的可视化辅助工具。