Consider the general cubic polynomial f(x) = x³ + ax² + bx + c, where a, b, and c are real numbers.

a. Show that f has exactly one inflection point and it occurs at x* = -a/3.

b. Show that f is an odd function with respect to the inflection point (x*, f(x*)). This means that f(x*) - f(x* + x) = f(x* - x) - f(x*), for all x.