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A relative (or local) maximum, for a function, is a point such that the value of the function at that point is greater than the values within a region on either side of it. It need not be a global maximum.

For example, consider a functions such as f(x) = 3*x - x^3

[it is shaped a bit like the letter S on its side].


Now f(1) = 2 is greater than all values of f(x) for x > -2. So the point (1, f(1)0 represents a relative maximum. However, for any x less than -2, f(x) is greater than f(1), and as x becomes more and more negative, f(x) becomes infinitely large. So f(1) cannot be a global maximum.

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No, since the equation could be y = x3 (or something similar) which will have a point of inflection at (0,0), meaning there is no relative maximum/minimum, as the graph doesn't double back on itself For those that are unfamiliar with a point of inflection <http://mathsfirst.massey.ac.nz/Calculus/SignsOfDer/images/Introduction/POIinc.png>


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In mathematics, the term "maximum" refers to the largest value in a given set of numbers or the highest point of a function within a specified domain. It can be used in various contexts, such as finding the maximum value of a dataset, the maximum height of a curve, or the optimal solution in optimization problems. The maximum can be either absolute (the highest value overall) or relative (the highest value in a local neighborhood).

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