Given that

Checking the continuity at x = -1:

LHL at x =-1,

RHL at x =-1,

Hence, f(x) is continuous at x =-1.

Checking the differentiability at x =-1:

LHD at x =-1,

RHD at x =-1,

∵ LHD = RHD

Hence, options A and B are correct.