We know that, If f(x) is differentiable at x=a, then it is continuous at x=a ⇒ If f(x) is not continuous at x=a, then it is not differentiable at x=a (a) is incorrect and (b) is correct. Now, (c) graph of f(x)=|x|
|x| is continuous on R but it makes a corner at x=0 ∴|x| is not differentiable at x=0 option (c) is correct. (d) f(x)=x−[x]={x} [fractional put function] Then, f′(l)≠l