Honestly, I haven't a bloody clue, and just out of curiosity, why is it just that \(\displaystyle ||p(x)||<\delta\) but \(\displaystyle ||p'(x)||\geq\epsilon\) instead of \(\displaystyle ||p(x)-p(a)||<\delta\) but \(\displaystyle ||p'(x)-p'(a)||\geq\epsilon\)?

Sorry, I know I should know this, but I barely scraped by analysis in undergrad :-(