Max/Min Terminology

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There’s a lot of strange terminology in math, and here’s one example that confuses students and teachers alike: the word maxima is the plural for of the work maximum. Similarly, minima is the plural form of minimum, and extrema is the plural form of extremum.

That means that you might speak of the maximum of a function that only has one, or several minima of another function.

Here are some examples of how to use these words:

The function $3-2x^2$ has an absolute maximum at $x=0$ .
Where are the local maxima of the function $\sin x$ ?
To find the extrema of a function $f$ , you first need to calculate the critical points. Once you’ve found the $x$ coordinate of one extremum, you can plug it back in to obtain the corresponding $y$ value.