Let f be a function such that f(x)=f(1-x) for all real numbers x.If f is differentiable everywhere,then f'(0)=?为什么是-f'(1)而不是f'(1)?

Let f be a function such that f(x)=f(1-x) for all real numbers x.If f is differentiable everywhere,then f'(0)=?为什么是-f'(1)而不是f'(1)?
Let f be a function such that f(x)=f(1-x) for all real numbers x.If f is differentiable everywhere,then f'(0)=?
为什么是-f'(1)而不是f'(1)?

Let f be a function such that f(x)=f(1-x) for all real numbers x.If f is differentiable everywhere,then f'(0)=?为什么是-f'(1)而不是f'(1)?
根据导数的定义来,f'(0)=Lim(h→0)[f(0+h)-f(0)]/h=Lim(h→0)[f(h)-f(0)]/h=Lim(h→0)[f(1-h)-f(1)]/h
=-Lim(h→0)[f(1-h)-f(1)]/(-h)=-f'(1),导数的定义式