Let f(x) = x^3 + ax^2 + bx + c where a, b, and c are constants with a>0 (or a=0) and b > 0.

a) Over what intervals is f concave up? Concave down?

b) Show that f must have exactly one inflection point.

c) Given that (0, -2) is the inflection point of f, compute a and c, and then show that f has no critical point.

Really lost. All help is greatly appreciated.