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Question

Let $f open parentheses x close parentheses equals square root of x minus 1 end root plus square root of x plus 24 minus 10 square root of x minus 1 end root end root comma blank 1 less or equal than x less or equal than 26$ be real valued function, then $f to the power of ´ end exponent left parenthesis x right parenthesis$ for $1 less than x less than 26$ is

0
$\frac{1}{\sqrt{x - 1}}$
$2 \sqrt{x - 1} - 5$
None of these

The correct answer is: 0

From Rolle’s theorem in given interval, [1,26], $f open parentheses 1 close parentheses equals open parentheses 26 close parentheses equals 5$ function satisfy all the condition of Rolle’s theorem, therefore in [1,26], at least, there is one point for which $f to the power of ´ end exponent open parentheses x close parentheses equals 0$

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