设这个式子为y,
整理后得到：y=3(1+t)(9t+1)/[(1+3t)^2]
=3(9t^2+10t+1)/[(1+3t)^2]
=[3(9t^2+6t+1)+12t]/(9t^2+6t+1)
=3+12t/(9t^2+6t+1)
=3+12/(9t+6+1/t)
要得到y(max)只需求出分母9t+6+1/t的最小值,6为常数,则求出9t+1/t最小值
因为t>=0,所以(3t-1)^2>=0,9t^2+1>=6t,9t+1/t>=6,只有在t=1/3最小
因此,当t=1/3时,y(max)=4