f'(x)=6x²+6ax+3b,则f'(1)=0且f'(2)=0,代入,解得a=-3,b=4,则f'(x)=6(x-1)(x-2).
f(x)在(-∞,1)上递增,在(1,2)上递减,在(2,+∞)上递增.要满足f(x)【f(x)】的最大值即可.