Editing Mathematical optimization (section)

=== Minimum and maximum value of a function ===
Consider the following notation:
:<math>\min_{x\in\mathbb R}\; \left(x^2 + 1\right)</math>

This denotes the minimum [[Value (mathematics)|value]] of the objective function {{math|''x''<sup>2</sup> + 1}}, when choosing {{mvar|x}} from the set of [[real number]]s <math>\mathbb{R}</math>. The minimum value in this case is 1, occurring at {{math|1=''x'' = 0}}.

Similarly, the notation

:<math>\max_{x\in\mathbb R}\; 2x</math>

asks for the maximum value of the objective function {{math|2''x''}}, where {{mvar|x}} may be any real number. In this case, there is no such maximum as the objective function is unbounded, so the answer is "[[infinity]]" or "[[Undefined (mathematics)|undefined]]".