A) 0
B) \[\frac{1}{\sqrt{x-1}}\]
C) \[2\sqrt{x-1}-5\]
D) None of these
Correct Answer: A
Solution :
[a] \[f(x)=\sqrt{x-1}+\sqrt{25+(x-1)-10\sqrt{x-1}}\] \[=\sqrt{x-1}+\sqrt{{{(5-\sqrt{x-1})}^{2}}}\] \[=\sqrt{x-1}+\left| 5-\sqrt{x-1} \right|=5\] \[[\because \sqrt{x-1}<5for1<x<26]\] \[\therefore f'(x)=0\]
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