Library of Functions: Intro to Derivatives - Slope Functions

① This example dynamically shows how the slope of a tangent line changes along a function's graph, visually introducing the derivative as a slope function. ② Core mathematical concepts include derivatives, tangent line slope, rate of change, and the transition from geometric intuition to calculus analysis. ③ Construction highlights: using GeoGebra commands Point (moving point on the function), Tangent (drawing tangent line), Slope (computing slope), and Segment (auxiliary segments), with objects f (original function), A (moving point), g (tangent line), m (slope value), S (slope function graph), and h, i, j (auxiliary objects) to build an interactive demonstration. ④ Suitable for high school and early college students beginning calculus, to understand the definition of derivative and the geometric meaning of slope functions, and also useful for classroom teaching.