The greatest integer function defined by f(x) = [2x], 0 < x < 2

The correct answer is Option (3) → differentiable except at the points $x=\frac{1}{2}, 1$ and $\frac{3}{2}$ in (0, 2)

greatest integer function is not differentiable at integral points

for $x∈(0,2)$

$2x∈(0,4)$

for $2x=1,2,3$

or $x=\frac{1}{2},1,\frac{3}{2}$

$[2x]$ → not differentiable