Question

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)

Answer 1

The right option is (c). The Mean Value Theorem does not apply since f(x) is not differentiable on (-1,8). Because the derivative of f is 2/3 x^(-1/3)  which is undefined at x=0.So, that would imply that it is not differentiable along the interval.