# 4 problems / if u can solve one of them i would really appreciate it /numerical

For problem 1, the proof is obvious by definition. If $f\in C^n(\Omega)$ then $f^\prime, f^{\prime\prime}, \ldots, f^{(n)}$ are all continuous. Let $g = f'$. Now, what are $f^{\prime\prime}, \ldots, f^{(n)}$ in terms of $g$? What does that tell you about $g$'s differentiability class?