若函数f(x)在x=0处连续,则(x趋向于零时),limf(x)=f(0).
此时,若:limf(x)/x(x趋向于零时)存在,必有:f(0)=0.
故:(x趋向于零时) lim{[f(x)-f(0)]/(x-0)}=lim{f(x)/x}
即知:f(x)在x=0处可导.