Continuity and differentiability of greatest integer function for JEE

Formula

\[[x]\text{ is continuous on }\mathbb R\setminus\mathbb Z,\text{ discontinuous at every integer, and }\frac{d}{dx}[x]=0\text{ for }x\notin\mathbb Z\]

Variables: \(\mathbb Z\) is set of integers.

Conditions: Derivative fails at integers due to discontinuity.

Standard graph, continuity and differentiability questions.