Let $f$ be a function such that $f'''$ is continuous and $f(0)=f'(0)=f'(1)=0$. Prove that there exists $c \in (0,1)$ such that
$$f(1)=-\frac{1}{12} f'''(c)$$
Let $f$ be a function such that $f'''$ is continuous and $f(0)=f'(0)=f'(1)=0$. Prove that there exists $c \in (0,1)$ such that
$$f(1)=-\frac{1}{12} f'''(c)$$