Extremal is an adjective that refers to something relating to or being an extreme or utmost condition, limit, or value within a given context. It describes things that are situated at or represent the furthest or highest point on a scale or spectrum, or possess qualities that deviate significantly from the norm or average.
In mathematics, the term "extremal" is commonly used to describe solutions or objects that optimize or minimize a certain property or function. An extremal point, for example, is a point on a curve where the tangent is parallel to the x-axis, representing a maximum or minimum value. Extremal problems involve finding the maximum or minimum value of a function subject to certain constraints or conditions.
In physics, "extremal" may refer to extreme states or conditions, such as extremely high or low temperatures, pressures, or energies. Extremal events in natural phenomena often represent rare or exceptional occurrences, like an extremal weather event or an extremal geological formation.
Furthermore, the term can be used in a more general context to describe actions, behaviors, or attitudes that are significantly far removed from what is considered typical, normal, or acceptable. For instance, an extremal viewpoint or position is one that takes an extreme stance or pushes boundaries beyond conventional limits.
Overall, the term "extremal" encompasses the concepts of being extreme, utmost, extraordinary, or deviating significantly from the average or expected.
