Prove there exists a $c \in (a,b)$ such that $\frac{f'(c)}{f(c)} = \frac{1}{a-c}+\frac{1}{b-c}.$
Let $f$ be continuous on $ [a,b]$, differentiable on $ (a,b) $ and $ f(x) \neq 0 \forall x \in (a,b) $ Prove $ \exists c \in (a,b) $ such that