Differentiability implies continuity, hence if a function is not continuous at a point, it is not differentiable either.
f(x) is continuous at x=1 because . This can be verified numerically, and by graphing.
f(x) will fail to be differentiable if does not exist.
You can numerically investigate the limit from the left, and the limit from the right. If the two match, then the function is differentiable. If they don't, it fails.
Graphically, if you have a corner or a cusp (since it is continuous) then it is not differentiable.
Follow a similar logic in the second problem.