Chapter 4: Applications of Derivatives - Section 4.2 - The Mean Value Theorem - Exercises 4.2 - Page 197: 9

Mean value Theorem has been satisfied.

Since, we have, $f(x)=\sqrt{x (1-x)}$ Also, $f'(x)=(\dfrac{1}{2})[(x(1-x))^{-1/2}((1-x)-x)]$ . This implies that the function $f(x)=\sqrt{x (1-x)}$ is continuous on $[0,1]$ and differentiable on $(0,1)$. Hence, the Mean value Theorem has been satisfied.