1
f'(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