I could use some help getting this proof going.

Let $\displaystyle f:R\rightarrow [0,\infty)$ be continuous. Suppose $\displaystyle lim_{x\rightarrow +\infty} f(x)=0$ and $\displaystyle lim_{x\rightarrow -\infty} f(x)=0$.

Prove that $\displaystyle f$ does not have a minimum on $\displaystyle R$ and

prove that $\displaystyle f$ has a maximum on $\displaystyle R$.