Method for structuring monotonically changing continuous functions based on examples of agro-industrial complex processes

A number of processes in the natural sciences, particularly in the agro-industrial complex, are described as monotonic continuous functions based on both theoretical and experimental frameworks. During the analysis of such dependencies, there arises a need to analyze the rate of their change over a certain interval of argument variation. This is often determined arbitrarily. We have developed a method for structuring a monotonic continuous function based on Lagrange's theorem to justify and distinguish be-tween significant, slightly significant, and insignificant sections. In this method, a point of significance is de-fined as a point of tangency of a line parallel to the segment connecting the initial and final points of the entire interval of the function definition, while a point of slight significance is defined as a point of tangency of a line parallel to the segment connecting the point of significance and the final point of the function's de-finition interval. There has been developed and presented an algorithm for implementing this method using examples from agro-industrial complex processes. When assessing the degree of mixing of ingredients for pig farming, we have determined the rational duration for measuring the total resistance of the feed mixture to direct current (the separating criterion). This measurement significantly changes up to 135 seconds and changes less significantly from 135 to 202.5 seconds, meaning that the desired value can be measured after 150 seconds. With a specific vertical load of up to 9.29 kPa, the steel friction coefficient for crushed sugar beet significantly changes (from 0.62 to 0.35), while from 9.29 to 13.25 kPa, it changes insignificantly (from 0.35 to 0.29). Therefore, for practical calculations, one should consider the change in the friction co-efficient under a vertical load of up to 13.25 kPa. When structuring the dependence of the specific cost of steamed feed for pigs, we have established a range of rational values for the useful capacity of a portioned circulation feed mixer at around 2.77 m³.