Zig zag/Continuity/Differentiability/Extrema/Exercise

Consider the function

$f:ℝ⟶ℝ,$

defined by

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

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

Create a solution