Zig zag/Continuity/Differentiability/Extrema/Exercise

Consider the function

$f\colon \mathbb {R} \longrightarrow \mathbb {R} ,$

defined by

${}f(x)={\begin{cases}x-\lfloor x\rfloor ,{\text{ if }}\lfloor x\rfloor {\text{ is even}},\\\lfloor x\rfloor -x+1,{\text{ if }}\lfloor x\rfloor {\text{ is odd}}\,.\end{cases}}\,$

Examine ${}f$ in terms of continuity, differentiability and extremes.

Create a solution