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?
The value of from the Lagrange's mean value theorem for which \( f(x) = \sqrt{25 - x^2} \) in the interval \( [1,5] \) is?
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The mean value theorem guarantees that there is at least one point in the interval where the derivative equals the average rate of change.
Updated On: Jan 12, 2026
- 5
- \( \sqrt{5} \)
- \( 3 \)
- None of these
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The Correct Option is C
Solution and Explanation
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.
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