Question 8
For real $a \lt b$, and $f : (a, b) \to \mathbb{R}$ a function such that the functions defined by $g : (a, b) \to \mathbb{R}$, $g(x) = (x-a)f(x)$, and $h : (a, b) \to \mathbb{R}$, $h(x) = (x-b)f(x)$ are non-decreasing, prove that $f$ is continuous.
Vladimir Cerbu and Sorin Rădulescu
Vladimir Cerbu and Sorin Rădulescu