若函数f(x)=-1/3x3+1/2f′(1)x2-f′(2)x+5,则曲线f(x)在点(0,f(0))处的切线方程为_.
问题描述:
若函数f(x)=-
x3+1 3
f′(1)x2-f′(2)x+5,则曲线f(x)在点(0,f(0))处的切线方程为______. 1 2
答
∵f(x)=-13x3+12f′(1)x2-f′(2)x+5,∴f′(x)=-2x2+f′(1)x-f′(2),∴f′(1)=-2+f′(1)-f′(2),f′(2)=-8+2f′(1)-f′(2),∴f′(1)=2,f′(2)=-2,∴f(x)=-13x3+x2+2x+5,f′(x...