Question

PROJECT:detail discussion on maxima minima of given function with special reference to the following cases: difference between local and global minima
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Answer 1

Step-by-step explanation:

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.

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.

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Answer 2

PROJECT: detail discussion on maxima minima of given function with special reference to the following cases: the difference between local and global minima

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• The maxima and minima (the separate plurals of greatest and least) of a capacity, referred to aggregately as extrema (the plural of extremum), are the biggest and littlest worth of the capacity, either inside a given reach (the neighborhood or relative extrema) or on the whole area (the worldwide or outright extrema).

• A genuine esteemed capacity f characterized on a space X has a worldwide (or outright) greatest point at x∗, if f(x∗) ≥ f(x) for all x in X. Essentially, the capacity has a worldwide (or outright) least point at x∗ if f(x∗) ≤ f(x) for all x in X.
• The worth of the capacity at the greatest point is known as the most extreme worth of the capacity, signified, and the worth of the capacity at any rate point is known as the base worth of the capacity.