This question seemed easy at first, except I keep getting stuck.

A curve with equation of the form y= ax^3 + bx^2 + cx + d has zero gradient at the point (1/3,4/27), and also touches, but does not cross, the x-axis at the point (1,0). Find a,b,c,d.

I suppose you differentiate and substitute the coordinates in, except there never seems to be enough information supplied.

Thanks!