The word ‘maxima’ is a plural of ‘maximum’ and the word ‘minima’ is the plural of minimum. Before we proceed further let us first discuss what a function is. A function is relation, subject to certain conditions, describes the output for a given input. In simple terms it is a ‘mathematical machine’ which converts the input and the type of conversion depends on the nature of the relation described in the function.
In any case, the output of a function varies with the variation of input except in case of constant functions. The output may increase or decrease or may undergo both. In many cases the phenomenon may repeat. When a function is increasing in an interval and starts decreasing subsequently, the changeover point represents the maximum value in the given interval. Hence we call that point as ‘local’ or ‘relative’ maximum. We use such a prefix because a similar situation may occur also in some other intervals in the domain of the function. In other words, a function can have a number of peak points which is collectively called as ‘maxima’ of the function. As the reverse case, a function can also have a number of local minimum points.