Is it possible to construct such a function? Just wondering.
Specifically, I am thinking of $f:\mathbb{R}\to\mathbb{R}$ such that $f'(0)$ exists and $f$ is discontinuous for all $x\in\mathbb{R}-\{0\}$.
2026-03-30 09:44:00.1774863840
Function differentiable at one point and nowhere else continuous.
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Consider
$$ f(x) = \left\{ \begin{array}{lr} x^2 & : x \in \mathbb{Q}\\ 0 & : x \notin \mathbb{Q} \end{array} \right. $$