What is the exact difference between $\arg\max$ and $\max$ of a function?
Is it right to say the following?
$\arg\max f(x)$ is nothing but the value of $x$ for which the value of the function is maximal. And $\max f(x)$ means value of $f(x)$ for which it is maximum.
$\arg \max$ returns a value from the domain of the function and $\max$ returns from the range of the function?