Differentiable function under specific topological constraints

Question

Can you give an example of a set$\:\:\emptyset\neq \mathcal D\large⊂$$\:\mathbb{\Re}\:$ and a differentiable function $\:f$ : $\mathcal D → \mathbb{\Re}\:\:$ such that $$\mathcal D ⊂ \text{Acc}(\mathcal D),\:\frac{\text d}{\text dx}f(x) = 0\:\:\forall x∈\left(\mathcal D \land f\right)\neq c \in\:\mathbb{\Re}$$.

This was a bonus question on my exam and I'd appreciate any given tips on how to find such an example.

Thanks!

Answer 1

Actually, my first example was massive overkill. Take $D = \mathbb{R} \setminus \{0\}$ and $$f(x) = \begin{cases} 1 & \text{x > 0} \\ -1 & \text{x < 0} \end{cases}$$