函数f(x)=ax³-x²+x-5在（-∞,+∞）上单调递增,求实数a的取值范围对f(x)求导,得f′(x)=3ax^2-2x+1,当且仅当y=3ax^2-2x+1在（-∞,+∞）恒大于0时,函数f(x)在（-∞,+∞）上单调递增.∴a＞0且△＜0,解得a＞1/3...