(1).f'(x)=3x^2+4ax+3.,f'(3)=3*3^2+4a*3+3=6(5+2a)=0,a=-5/2<1,条件有误
f'(x)=3x^2-10x+3=(3x-1)(x-3),令f'(x)=0,得x=3或1/3,
(2).f'(x)=3x^2+4ax+3为开口向上的二次函数,
若[1,+无穷)上f(x)是增函数,
则f'(1)>=0,且对称轴x=-2a/3<=1,
即6+4a>=0且a>=3/2
即a>=-3/2且a>=3/2
a的取值范围为[-3/2,3/2]