First Derivative Functions: Tangent Slope and Derivative Graph

① This example dynamically demonstrates how the first derivative function is generated by tracing the slope of the tangent line at a moving point on the original function's graph. ② Core mathematical concepts include the geometric meaning of the derivative, tangent slope, the relationship between a function and its derivative, and the use of similar triangles to visualize slope changes. ③ Construction details: GeoGebra commands such as Point, Tangent, Slope, and Derivative are used, involving objects like the original function f, moving point A, tangent line g, slope m, derivative function f', and auxiliary objects a, b, c, d, D', Deri. The dynamic behavior is controlled by sliders or dragging points. ④ Suitable for high school calculus introduction and college-level elementary calculus, useful for understanding the definition of the derivative and curve sketching, as well as classroom demonstrations of differential calculus.