Consider the function f(x) = x^{2/3} on the interval [-1,8].

determine whether or not f(x) satisfies the conditions of the mean value theorem for its given interval. select the most correct answer from the choices below:

(a). the mean value theorem applies for f(x) on [-1,8].
(b). the mean value theorem does not apply since f(x) is not continuous on [-1,8].
(c). the mean value theorem does not apply since f(x) is not differentiable on (-1,8).
(d). the mean value theorem does not apply since f(x) is not continuous on [-1,8] and not differentiable on (-1,8)