Final answer:
The Mean Value Theorem cannot be applied to the function √(4-x) on the interval [-5, 4] because the function is not differentiable at the endpoint x = 4.
Step-by-step explanation:
Applying the Mean Value Theorem
The Mean Value Theorem (MVT) states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there is at least one number c in the interval (a, b) such that f'(c) is equal to the average rate of change of the function over that interval.
For the function f(x) = √(4-x), we need to examine whether it satisfies the continuity and differentiability criteria on the interval [-5, 4]. The function is continuous on this interval, because the square root function is continuous wherever it is defined, which in this case is for x ≤ 4. However, differentiability is a concern because the square root function is not differentiable at the endpoint x = 4. Since the function is not differentiable over the entire interval (a, b), the MVT cannot be applied to f(x) = √(4-x) on the interval [-5, 4].