In mathematical analysis, the maximum and minimum[a] of a function are, respectively, the greatest and least value taken by the function.

Extrema (maximum and minimum values) are important because they provide a lot of information about a function and aid in answering questions of optimality. Calculus provides a variety of …

Notice that when a function is defined on a closed interval, an absolute extreme value may occur at the endpoint of that interval of domain, since the endpoint of the interval may yield the …

The plural of extremum is extrema and similarly for maximum and minimum. Because a relative extremum is “extreme” locally by looking at points “close to” it, it is also referred to as a local …

At this point, we know how to locate absolute extrema for continuous functions over closed intervals. We have also defined local extrema and determined that if a function f has a local …

Illustrated definition of Extrema: The smallest and largest values (within a given domain): The plural of Minimum is Minima The plural...

extremum, in calculus, any point at which the value of a function is largest (a maximum) or smallest (a minimum). There are both absolute and relative (or local) maxima and minima.

Problem 13.1: Find all the extrema of the function f(x, y) = 3x ∗ y + x2 ∗ y + x ∗ y2 they are maxima, minima or saddle points.

Dec 3, 2025 · Functions with many extrema can be very difficult to graph. Notorious examples include the functions and near , plotted above. Another pathological example is near 0 and 1, …

If we seek to know if and where such extrema occur (both local and absolute), we should be aware of the following two important results. The first gives us a sufficient (but not necessary) …