已知函数f(x)的导数为f′(x),且满足f(x)=3x2+2xf′(1),则f′(3)=(  ) A.9 B.6 C.-6 D.20

问题描述:

已知函数f(x)的导数为f′(x),且满足f(x)=3x2+2xf′(1),则f′(3)=(  )
A. 9
B. 6
C. -6
D. 20

f′(x)=6x+2f′(1),
令x=1,得f′(1)=6+2f′(1),解得f′(1)=-6,
则f′(x)=6x-12,
所以f′(3)=6×3-12=6,
故选B.