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Question: Let f(x) = \(\sqrt{x - 1}\) + \(\sqrt{x + 24 - 10\sqrt{x - 1}}\), 1 \< x \< 26 be real valued funct...

Let f(x) = x−1\sqrt{x - 1} + x+24−10x−1\sqrt{x + 24 - 10\sqrt{x - 1}},

1 < x < 26 be real valued function, then f ¢(x) for 1 < x < 26 is

A

0

B

1x−1\frac{1}{\sqrt{x - 1}}

C

2x−1\sqrt{x - 1} – 5

D

None of these

Answer

0

Explanation

Solution

f(x)x−1+x+24−10x−1\sqrt{x - 1} + \sqrt{x + 24 - 10\sqrt{x - 1}}Žx−1+(5−x−1)2\sqrt{x - 1} + \sqrt{(5 - \sqrt{x - 1})^{2}}

x−1+∣5−x−1∣,\sqrt{x - 1} + |5 - \sqrt{x - 1}|,1< x < 26

Ž x−1+(5−x−1)\sqrt{x - 1} + (5 - \sqrt{x - 1}) Ž dy/dx = 0