maximum
A local maximum of a function is a value that is greater than or equal to all nearby values of the function, while a local minimum is a value that is less than or equal to all nearby values. Similarly, a global maximum is a value that is greater than or equal to all values of the function within its entire domain, and a global minimum is a value that is less than or equal to all values of the function within its entire domain.
Applications
In applications, the identification of maximum and minimum values of a function is crucial for understanding its behavior and for solving practical problems. These extrema can represent optimal conditions such as maximum profit or minimum cost, which are essential in various fields including economics, engineering, and the physical sciences.