If f(x)=|logx10|∀ x ϵ(0,∞) then
f(x) is continuous but not differentiable in (0, ∞)
Clearly, we see f(x) is continuous from (0,∞) but there is a sharp edge at 1 which means LHD and RHD
are finite but not equal. Therefore f(x) is continuous in (0,∞) but not differentiable throughout (0,∞). It
is only differentiable in xϵ(0,1) ∪ (1,∞).