Mean-value theorem

Exercise

1.

Find the admissible value $\xi$ of the following function and interval.

(a)

$${f(x) = x^{3} - x^{2}, \ [-1,1]}$$

(b)

$${f(x) = \sin^{-1}{x}, \ [0,1]}$$

(c)

$${f(x) = \log{x}, \ [1,e]}$$