设函数f(x)满足f(x)=-f(x+2),且图像在点(1,f(1))处的切线与x轴平行,则曲线y=f(x)在x=2013处的切线的斜率为
问题描述:
设函数f(x)满足f(x)=-f(x+2),且图像在点(1,f(1))处的切线与x轴平行,则曲线y=f(x)在x=2013处的切线的斜率为
答
f(x)=-f(x+2)=f(x+4),
f(x)周期为4,
k=f'(2013)=f'(1)=0