The aim of investigation was to seek new ways for the analysis of extremal problems. A method of visual analysis of a set of objective function values is proposed. It allows us to find a direction where the variation of function is maximal. The method ensures a high quality of analysis when the number of used values of the objective function is small, and a possibility of identifying a specific character of the objective function. The results of analysis are used in search of a new coordinate system of the extremal problem and in a graphical representation of the observed data. The analysis will lead us to a better optimization strategy.