Determinw wheather the mean value theorem applies to the function f(x)= 6x^1/3 on the interval [-8,8]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem.

Answer 1

f(x) = 6x^1/3

f'(x) = 2x^-2/3 = 2 / x^2/3

f'(x) is undefined at x = 0, so f(x) is not differentiable there.

Since f(x) is not differentiable on the entire interval (-8,8), the Mean Value Theorem can not be applied.