Let $$X$$ be a subset of $$\mathbb{R}$$, and let $$x_0 \in X$$ be a limit point of $$X$$. Let $$f: X \to \mathbb{R}$$ be a function. If $$f$$ is [...] and is [...], then $$f'(x_0) \ge 0$$.
If instead, $$f$$ is monotone decreasing, then $$f'(x_0) \le 0$$.