若函数f(x)定义域为R且f(x)=ex+x2-x+sinx,则曲线y=f(x)在点(0,f(0))处的切线方程是_.
问题描述:
若函数f(x)定义域为R且f(x)=ex+x2-x+sinx,则曲线y=f(x)在点(0,f(0))处的切线方程是______.
答
求导函数可得f′(x)=ex+2x-1+cosx,
当x=0时,f′(0)=e0-1+cos0=1,
∵f(0)=e0+sin0=1,∴切点为(0,1)
∴曲线y=f(x)在点(0,f(0))处的切线方程是y-1=1•(x-0),即y=x+1
故答案为:y=x+1