Root Point Analysis of a Function and Its Derivatives: C0306X38

This GeoGebra example demonstrates how to use the Roots command to find the roots of a function f and its first and second derivatives f' and f'', thereby supporting curve sketching and analysis. The core mathematical concepts include zeros of functions, the geometric meaning of derivatives (extrema and inflection points), and calculus-based curve analysis. The construction uses the GeoGebra Roots command on f, f', and f'' to generate root objects (Roots, Roots1, Roots2), which mark intersections with the x-axis, critical points, and inflection points. This is suitable for high school to university-level calculus instruction, helping students visualize the relationship between a function and its derivatives, and can be used for exercise verification or classroom demonstrations.