Condition (1):

Since, f(x)=2+(x-1)^2/3 is a polynomial and we know every polynomial function is continuous for all xϵR.

⇒ f(x)= 2+(x-1)^2/3 is continuous on [0,2].

Condition (2):

Here, which does not exist at x=1 in [0,2].

f(x)= 2+(x-1)^2/3 is not differentiable on (0,2).

Condition (2) of Rolle’s theorem is not satisfied.

So,Rolle’s theorem is not applicable.