Tangent Slope and Derivative Y-Value Correspondence

① This example dynamically demonstrates the correspondence between the slope of the tangent line to a function f and the y-value of its derivative f', while also showing the graph of the second derivative f'' to deepen understanding of the geometric meaning of derivatives as instantaneous rates of change. ② Core mathematical concepts include derivatives, tangent slopes, second derivatives, and relationships among function graphs, rooted in fundamental definitions and geometric interpretations in calculus. ③ Construction highlights: using GeoGebra commands Point, Tangent, Segment, OrthogonalLine, Intersect, and Slope to construct the tangent line and measure its slope; plotting the three curves f, f', and f''; moving point A along f dynamically updates the tangent line g and the slope value, with text objects text1 and text2 displaying the numerical correspondence. ④ Suitable for high school and early college students learning calculus, ideal for classroom demonstrations or self-exploration to build an intuitive link between derivative notation and graphical slope.