已知函数f(x)=x^3-ax^2+3x

1f'(x)=3x^2-2ax+3;则在[1,+无穷)上,有f'(x)=3x^2-2ax+3≥0;则:f'(1)=3-2a+3=6-2a≥0→a≤3且在[1,+无穷)上,有f''(x)=6x-2a≥0。→x≥a/3。则a/3≤1;→a≤3实数a的取值范围是a≤3。2若x=3是f(x)的极值点,且f'(x)=3x^2-2ax+3连续,则f'(3)=27-6a+3=0则a=5。f(x)=x^3-5x^2+3x;f'(x)=3x^2-10x+3;使f'(x)=3x^2-10x+3=0,则x=3或x=1/3。而f''(x)=6x-2a=6x-10则f''(3)=6*3-10=8>0,则x=3是f(x)的极小值;极小值f(3)=-9。f''(1/3)=6/3-10=-8