Forf(x)=(x−1)2/3 , the mean value theorem is applicable tof(x) in the interval

Sincef'(x) does not exist atx=1 , ( f'(x)=23(x−1)−1/3) therefore, mean value theorem is not applicable to the given function in any interval which contains 1 as an interior point. SO, in this case the required interval is[2,4] .