# What is an extremum?

Extreme is a mathematical term thatis used to describe the mathematical function or graph of this function. Let's define what is an extremum. This is the minimum value of any mathematical function in a given numerical set.

Accordingly, the point of the graph of the function in whichthe function itself reaches an extremum, is called the extremum point (the minimum or maximum point). Also in mathematics such term as local and absolute extremum is used.

Not all functions can have minimal andmaximum extremes. So the function ƒ, which is constructed from a numerical set M, may not have local or absolute extrema. For example, such a function should be given by the formula: ƒ (x) = x, where x lies in the region between the minus unit and the unit - x Є (-1; 1). Hence it follows that there must be conditions for the presence of extrema. One of the conditions for the existence of an extremum is the existence of the derivative of a given function.

In order to solve a mathematical problem with this function, it will be useful to read our article. How to find the extremum.