Question 52
Let $u : [a, b] \to \mathbb{R}$ be a continuous function which has at each point $x \in (a, b]$ a finite left derivative, denoted by $u'_s(x)$. Prove that the function $u$ is increasing if and only if $u'_s(x) \ge 0$, for all $x \in (a, b]$.