In this paper,we mainly discuss the approximating relation between the extremums (points) of functions sequence {f_n(x)} and the limiting function f(x).Firstly,by the analysis of actual examples,we give the convergence condition when the extremum ponits of f_n(x) and f(x) are unique.Furthermore,we introduce the concepts of ε-approximation maximum (of minimum) value point,and also give the approximation theorem about the extremum points of {f_n(x)} and f(x) under the approximate-optimal condition.