First slide

Derivatives

Question

$f (x) = \sqrt{x - 1} + \sqrt{x + 24 - 10 \sqrt{x - 1}} (1 < x < 26) then f^{'} (x) =$

Moderate

A

0
B

$\frac{1}{\sqrt{x - 1}}$
C

$2 \sqrt{x - 1} - 5$
D

1

Solution

$\begin{aligned} f (x) = \sqrt{x - 1} + \sqrt{x + 24 - 2 \sqrt{25 (x - 1)}} = \sqrt{x - 1} + \sqrt{25} - \sqrt{x - 1} = 5 \end{aligned}$
$\Rightarrow f' (x) = 0$

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