Question

The value of \( x \) in the interval \( [4, 9] \) at which the function \[ f(x) = \sqrt{x} \] \text{satisfies the mean value theorem is:}

• A. \( \frac{13}{4} \)
• B. \( \frac{17}{4} \)
• C. \( \frac{21}{4} \)
• D. \( \frac{25}{4} \)

Hint:

The mean value theorem states that there exists a point where the derivative equals the average rate of change.

Answer 1

The Correct Option is B

Using the mean value theorem, calculate the derivative of \( f(x) \) and solve for \( x \) in the interval \( [4, 9] \).
Final Answer: \[ \boxed{\frac{17}{4}} \]