University Calculus: Early Transcendentals (3rd Edition)

Here, $f(x)=x^{\frac{2}[3}$and $f'(x)=\dfrac{2}{3x^{1/3}}$ . This means that the function is undefined at $x=0$; thus, it is not differentiable at $x=0$. Thus, the Mean Value Theorem does not satisfy.