Answer
The function is not differentiable on the interval $(-1,1)$. The hypotheses of Rolle's Theorem are not satisfied.
Work Step by Step
$f(x) = 1-x^{2/3}$
$f'(x) = -\frac{2}{3x^{1/3}}$
The derivative does not exist when $x = 0$. Thus, the function is not differentiable on the interval $(-1,1)$. The hypotheses of Rolle's Theorem are not satisfied.
Therefore, the fact that there is no number $c$ in the interval $(-1,1)$ such that $f'(c) = 0$ does not contradict Rolle's Theorem.
