Let $f:[2,7] \rightarrow \Bbb{R}$ be a continuous function and for given $\epsilon >0$,we have to prove that there exists a polynomial $p$ such that $f(2)=p(2)$, $p'(2) = 0$ and $Sup\{|p(x) - f(x)|\}<\epsilon$. I think that this follows from the Weierstrass approximation theorem ($p$ approximate...