With GeoGebra you can investigate roots, local extrema and inflection points of polynomial functions.
f(x) = x^3 - 3 x^2 + 1
N = Root[f]
E = Extremum[f]
W = InflectionPoint[f]
In Move mode you can drag the function f with the mouse. In this context, the first two derivatives of f are interesting too.
Derivative[f]
Derivative[f, 2]