continuous ....no need to varify...for differentiability let solve...
f'(c)=limh->0+ (f(c+h)-f(c)/h) -> limh->0+ (1+h)3-1 -0 / h -> limh->0+ 1+h3+3h(h+1)-1/h ->limh->0+ h2+3(h+1) =3
limh->0- (f(c+h)-f(c)/h) -> limh->0- 1+h-1-0/h -> limh->0- 1=1 ....similarly for h->0
therefor not differentiable.