Problem
If $f(x)$ is continuous over $(a,+\infty)$, and $\lim\limits_{x \to a+}f(x)=+\infty,$$\lim\limits_{x \to +\infty}f(x)=+\infty,$ then $f(x)$ can reach its minimum value over $(a,+\infty)$.
This is my proof, which is written in Chinese. If necessary, I'm willing to translate it into English. But I hope to see your solutions.Thank you all!
