Is there a relationship between the stationary points and the inflection point of a cubic polynomial function? Determine the stationary points, A and B, and point of inflection, G, for each of the following cubic polynomials.
(a) $y=x^3 -3x^2 -9x+7$ 
(b) $y=x^3 -12x^2 +21x-14$
(c) $y=x^3 +9x^2 -12$
Is there any common relationship between A, B and G?

The first derivative of a cubic polynomial is a quadratic polynomial $q$, and as such is even with respect to its stationary point $\xi$. It follows that the real zeros of $q$, if there are any, are at equal distance on both sides of $\xi$. This implies $G={A+B\over2}$.
