Rolle’s Theorem states that,
The function f(x) must be continuous in [-1,1], differentiable in (-1,1). and f(-1) = f(1)
F(x) isn’t differentiable at x=0, as f’x = -2/3 x^-1/3 , so f(x) doesn’t satisfy rolle’s theorem.
G(x) satisfy all conditions
H(x) doesn’t satisfy f(-1) = f(1)