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

Question

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?

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 02:45

score 5 · Accepted Answer · answered Oct 11 '13 at 22:06

5

It's often called the 'arg max' ('argument maximum'; similarly 'arg min'):

answered Oct 11 '13 at 22:06

BaronVT

1

Thanks. This seems well accepted enough. – Vortico Oct 11 '13 at 22:08
1

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

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