若函數f(x)=13x3+12f′(1)x2-f′(2)x+3,則f(x)在點(0,f(0))處切線的傾斜角為() A.π4B.π3C. 2π3D. 34π

若函數f(x)=13x3+12f′(1)x2-f′(2)x+3,則f(x)在點(0,f(0))處切線的傾斜角為() A.π4B.π3C. 2π3D. 34π

解析:由題意得: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)在點(0,f(0))處切線的斜率為-1,∴傾斜角為34π.故選D.