What Is a Floor Limit?

Lower limit, generally refers to the minimum value of the function or the minimum value of the independent variable. In mathematical analysis, within a given range (relative extreme value) or the entire domain of the function (global or absolute extreme value), the maximum and minimum values of the function The values are collectively called extreme values (extreme number). Pierre de Fermat was one of the first mathematicians to propose the maximum and minimum values of a function.

In mathematical analysis, within a given range (relative extreme value) or the entire domain of a function (global or absolute extreme value), the maximum and minimum values of a function are collectively referred to as the extreme value (extreme number). Pierre de Fermat was one of the first mathematicians to propose the maximum and minimum values of a function.

As defined in set theory, the maximum and minimum values of a set are the largest and smallest elements in the set, respectively. Infinite sets, such as real numbers, have no minimum or maximum. ^[1]

Finding the global maximum and minimum is the goal of mathematical optimization. If the function is continuous over a closed interval, there are global maximums and minimums through the minimum value theorem. In addition, the global maximum (or minimum) must be a local maximum (or minimum) within the domain, or it must be on the boundary of the domain. So the way to find the global maximum (or minimum) is to look at all local maximums (or minimums) inside, and also look at the maximum (or minimum) of the points on the boundary, and take the maximum or minimum) One.

Fermat's theorem can find differential functions of local extremes, which states that they must occur at critical points. It is possible to distinguish whether the critical point is a local maximum or a local minimum by using a first derivative test, a second derivative test, or a higher order derivative test, giving sufficient distinguishability.

For any function defined by segments, find the maximum (or minimum) by finding the maximum (or minimum) of each part separately, and then see which one is the maximum (or minimum).