Chapter 4: Applications of Derivatives - Section 4.2 - The Mean Value Theorem - Exercises 4.2 - Page 197: 7

Does not satisfy

Since, we have, $f(x)=x^{\frac{2}[3}$ Also, $f'(x)=\dfrac{2}{3x^{1/3}}$ . This implies that the function is undefined at $x=0$. So, this is not differentiable at $x=0$. Hence, The Mean value Theorem does not satisfy.