Using Theorem 1, prove that $F^{\prime}(x)=f(x)$ where $f(x)$ is a polynomial of degree $n-1,$ then $F(x)$ is a polynomial of degree $n .$ Then prove that if $g(x)$ is any function such that $g^{(n)}(x)=0,$ then $g(x)$ is a polynomial of degree at most $n$.