f(x+h)=f(x)+hf'(x+th)两边对h求导得:f’(x+h)=f'(x+th)+thf''(x+th)f’(x+h)-f'(x)=f'(x+th)-f'(x)+thf''(x+th)(f’(x+h)-f'(x))/h=t(f'(x+th)-f'(x))/th+tf''(x+th)令h趋于0,取极限得:f''(x)=limtf''(x)+limtf''(x)所以lim(h趋于0)t=1/2