Suppose $f:E \rightarrow \mathbb{R}$ is continuous at $p$. Prove that if $f(p) > 0$, then there is $\delta>0$ s.t. $f(x) \geq f(p)/2$ $\forall x$ in $E$ s.t. $|x-p| \leq \delta$.
I couldn't find other questions like it and I can't quite figure it out. I recognize that I am given that $f$ is continuous and so that allows me to play with the $\delta$ and $\epsilon$ to try and make the desired result pop up but i'm not quite sure how to. Any help would be appreciated.