In an exercise I have to make I am asked to show that a function $f$ has a global maximum and minimum, given that:
$f:\mathbb{R}\to\mathbb{R}$ is continuous and
$$\lim_{x\to\infty}f(x)=0.$$
However, in my mind, the function $f(x)=e^{-x^2}$ satisfies those conditions and has an global maximum, but no minimum at all.
Am I misinterpreting the given information?
Yes you are correct, in that case by the EVT we can only claim that the function has (at least) a maximum or a minimum.