I am having trouble showing the following.
Let $f$ be a continuously differentiable function on the closed interval $[0,1]$. Prove that for every $\epsilon >0$ there exists a polynomial $P$ such that \sup_{0 \le x\le 1} |f(x)-P(x)|+\sup_{0 \le x \le 1} |f'(x)-P'(x)| \le \epsilon.
Any hint or suggestion?