Discuss about the terms “Maxima and Minima”, explain by suitable example.(In mathematics engineering).Complete solution in full detail.
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Answer:
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema).[1][2][3] Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.
Local and global maxima and minima for cos(3πx)/x, 0.1≤ x ≤1.1
As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum.
