(Solved): Determine whether the Mean Value theorem can be applied to \( f \) on the closed interval \( [a, b] ...

Determine whether the Mean Value theorem can be applied to \( f \) on the closed interval \( [a, b] \). (Select \[ f(x)=x^{6}, \quad[-1,1] \] Yes, the Mean Value theorem can be applied. No, \( f \) is not continuous on \( [a, b] \). No, \( f \) is not differentiable on \( (a, b) \). None of the above. If the Mean Value theorem can be applied, find all values of \( c \) in the open interval \( (a, b) \) such that \( f^{\prime}(c) \) cannot be applied, enter NA.)