Abstract: In this paper, the asymptotic behavior of intermediate points is discussed for the differential mean value theorem of functions of several variables, which brings about more general results such as:
1)when ξ=x₀+θh(0 < θ < 1) then ???19960212???(||ξ-x₀||)/(||h||)=(1)/(2).
2)As the moving point x₀+h tends to x₀ along a certain direction,there are intermediate points ξ not belonging to the joining line between x₀ and x₀+h, the ξ, tends to x₀ along another define direction. In this case,
???19960212???(||ξ-x₀||)/(||h||)=(1)/(2) ((p⁰)^τ▽²f(x₀)p⁰)/((ξ⁰)^τ▽²f(x₀)p⁰)