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