# global max and min as limit to +-infinity equals 0

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?

• You are right, another counter-example is $\frac{1}{x^2+1}$. – Yanko Dec 7 '18 at 14:57