Question

The value of from the Lagrange's mean value theorem for which \( f(x) = \sqrt{25 - x^2} \) in the interval \( [1,5] \) is?

• A. 5
• B. \( \sqrt{5} \)
• C. \( 3 \)
• D. None of these

Hint:

The mean value theorem guarantees that there is at least one point in the interval where the derivative equals the average rate of change.

Answer 1

The Correct Option is C

The value of \( f'(x) \) is derived from the derivative of the given function and applying the mean value theorem. We find that the value at \( x = 3 \) satisfies the condition.