We fix $f \in \mathcal{C}^K([0,1])$ and denote by $P$ the polynomial determined in question Q7. For all $k \in \llbracket 0, K-1 \rrbracket$, show that there exist at least $K - k$ distinct real numbers in $[0,1]$ at which the function $f^{(k)} - P^{(k)}$ vanishes.