若函数f(x)=13x3+12f′(1)x2-f′(2)x+3,则f(x)在点(0,f(0))处切线的倾斜角为(  ) A.π4 B.π3 C.2π3 D.34π

问题描述:

若函数f(x)=

1
3
x3+
1
2
f′(1)x2-f′(2)x+3,则f(x)在点(0,f(0))处切线的倾斜角为(  )
A.
π
4

B.
π
3

C.
3

D.
3
4
π

解析:由题意得:f′(x)=x2+f′(1)x-f′(2),
令x=0,得f′(0)=-f′(2),
令x=1,得f′(1)=1+f′(1)-f′(2),
∴f′(2)=1,∴f′(0)=-1,
即f(x)在点(0,f(0))处切线的斜率为-1,
∴倾斜角为

3
4
π.
故选D.