Abstract: This papermakes qualitative research on the p rogressiveness of the intermediate point of Largrange mean value theorem. By studying the situation of f ( ×) in ( a, b) low order derivableness, we found that f ( x) in ( a, b) low order derivative can be popularized to the situation of n order continuous derivableness, furthermore, that positive integer n can be popularized to positive real number m, a more generalized conclusion is arrived at: lim b→a ξ- a b - a m 1 m + 1