Lebl-Basic-Analysis-I · Problem 4.1.5

The Derivative

Mathematics · differentiability-pathological

Problem

Define f:R→Rf : \mathbb{R} \to \mathbb{R} by f(x):={x2if x∈Q,0otherwise.f(x) := \begin{cases} x^2 & \text{if } x \in \mathbb{Q}, \\ 0 & \text{otherwise.} \end{cases} Prove that ff is differentiable at 00, but discontinuous at all points except 00.

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