Find a cubic function of the form f(x) = ax^3 + bx^2 + cx which has a local maximum at f(1) = 0 and a local minimum at f(3) = -2.

I'm stumped out of my mind. I'm pretty sure that both b and c must be negative, but beyond that, no matter how I munge and funge that function, I can't get it to behave. Is there some voodoo calculus trick that I'm missing here?

(I've tried solving the coefficients as a system of equations, but that didn't work. Every time I got it down to one variable with substitutions, the variable would cancel out, leaving me with something stupid like -2=-2. But, maybe I did it wrong.)

Thanks guys.