Mean-value theorem

Exercise

1.: Find the admissible value $\xi$ of the following function and interval.
(a): $\displaystyle{f(x) = x^{3} - x^{2}, \ [-1,1]}$
(b): $\displaystyle{f(x) = \sin^{-1}{x}, \ [0,1]}$
(c): $\displaystyle{f(x) = \log{x}, \ [1,e]}$