Let $n$ be a positive integer and $x:=(x_1,x_2,\ldots,x_n)$. For non-negative $x_1,x_2,\ldots,x_n$, consider the function value of $f(x)=x_1+x_2+\cdots+x_n$ subject to the constraint $x_1x_2\cdots x_n=1.$ What I want to know is, does $f(x)$ have:
A global maximum?
A global minimum?