Let $f\left(x\right)=[{\sin }^{4}x]$. Then (where $[.]$ represents the greatest integer function)

$f\left(x\right)$ is continuous at $x = 0$

$f\left(x\right)$ is differentiable at $x = 0$

$f\left(x\right)$ is continuous and not differentiable

$f\left(x\right)$ is not continuous at $x = 0$