If the function f(x) has LHD and RHD at x0, which are finite and equal, then f(x) is differentiable at x0, always.
True
Fit is not sufficient for LHD and RHD to be equal rthe function f(x) must be continuous at x0.
For example, consider the function f(x)=x2x.
LHD at x=0 is 1
RHD at x=0 is 1
But f(x) is not difined at x=0 i.e., f(x) is discontinuous at z=0 it is not differentiable at x=0