# Is there a name for the value $x$ such that $f(x)$ is maximum?

Obviously, $f(x)$ is called the "maximum value" or simply "maximum", but what is $x$ called? The maximizer?

Additionally, what if $f(x)$ is minimum or simply an extremum?

• "maximizer" sounds fine to me. – David Mitra Oct 11 '13 at 22:04
• The Maximizer strikes again... – copper.hat Oct 11 '13 at 22:31
• Sometimes known as the $\arg \max$, albeit this is usually the set of parameters that attain the maximum. – copper.hat Oct 11 '13 at 22:32
• "Parameter that attains the maximum" is also a good term for the case that learning potentially new terminology is not the scope of a paper. – Vortico Oct 12 '13 at 2:45

• Technically, arg max is the set of maximizers. This is true even if the maximizer $x^*$ is unique, that is, if $f(x^*)>f(x)$ for any $x\neq x^*$ in the domain of $f$. In this case, you could call $x^*$ the maximizer and $\{x^*\}$ the arg max. Despite the abuse of terminology, however, $x^*$ is often simply called the arg max anyway. – triple_sec Oct 11 '13 at 23:52