Consider the following function

$f(x)=|x-2|(x-5)|x-5|$

Choose the right statement about the continuity$/$differentiability of the function

$($i$)$ at $x=2,$ and

$($ii$)$ at $x=5$

A$.($i$)$ continuous and differentiable

$($ii$)$ continuous and differentiable

B$.($i$)$ continuous but not differentiable

$($ii$)$ continuous and differentiable $($CORRECT$)$

C$.($i$)$ continuous and differentiable

$($ii$)$ continuous but not differentiable

D$.($i$)$ not continuous but differentiable

$($ii$)$ continuous and differentiable

E$.($i$)$ continuous but not differentiable