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)?
来源:学生作业帮助网 编辑:作业帮 时间:2024/10/08 00:52:33
x)I-QHSHJUHTH+K.S(.MP(HhThڦiVh*)$(&(&+Tyg+dd&&*Ug EtJ2R54mdwÓfjhym(]_`g3Hقz=]
g<]7gs@Lx6@3:M@;CSHig7d 2m!As=6yv P<
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