Let f(x)=(x+|x|)|x| .  Then for all x

Give that f(x)={(x−x)(−x)=0x<0(x+x)x=2x2x≥0 As is evident from the graph of f(x)   that it is continuous and differentiable for all x.  Alsof'(x)={0x<04xx≥0 ∴ f'(x)  is continuous for all x but it is not differentiable at x=0 .