First slide

Derivatives

Question

$If f (x) = \sqrt{a x} + \frac{a^{2}}{\sqrt{α x}}, then f^{'} (a) =$

Moderate

A

a
B

0
C

1
D

-1

Solution

$f' (x) = \sqrt{a} \times \frac{1}{2 \sqrt{x}} + a \sqrt{a} (- \frac{1}{2}) x^{- 3 / 2} \Rightarrow f' (a) = \sqrt{a} \times \frac{1}{2 \sqrt{a}} - \frac{1}{2} a \sqrt{a} a^{- 3 / 2} = \frac{1}{2} - \frac{1}{2} = 0.$

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