Suppose $f(x)$ is continuous on a closed interval $[a,b]$ and differentiable on the open interval $(a,b)$. I would like to prove the existence of $c$ such that
$$ (c-a)\cdot(b-c)\cdot\ f'(c) = (2c-a-b)\cdot\ f(c) $$ and $a
Suppose $f(x)$ is continuous on a closed interval $[a,b]$ and differentiable on the open interval $(a,b)$. I would like to prove the existence of $c$ such that
$$ (c-a)\cdot(b-c)\cdot\ f'(c) = (2c-a-b)\cdot\ f(c) $$ and $a