设函数f(x)具有二阶连续导数,且f"(x)不等于0.

根据泰勒公式
f(x+h)=f(x)+f'(x)h+(1/2)f''(x)h^2+o(h^2)
于是：f(x)+hf'(x+θh)=f(x)+f'(x)h+(1/2)f''(x)h^2+o(h^2)
θ{[f'(x+θh)-f'(x)]/θh}=(1/2)f''(x)+o(h^2)/h^2
lim(h→0)θ{[f'(x+θh)-f'(x)]/θh}=lim(h→0)[(1/2)f''(x)+o(h^2)/h^2]
lim(h→0)θf''(x)=(1/2)f''(x)
lim(h→0)θ=1/2