If f(x)= x-4 2 x then f'(1) is equal to: - Vidyadip

MCQ

If $\text{f}(\text{x})=\frac{\text{x}-4}{2\sqrt{\text{x}}}$ then $f'(1)$ is equal to:

✓
$\frac{5}{4}$
B
$\frac{4}{5}$
C
$1$
D
$0$

✓

Answer

Correct option: A.

$\frac{5}{4}$

Given that $\text{f}(\text{x})=\frac{\text{x}-4}{2\sqrt{\text{x}}}$
$\therefore\text{f}(\text{x})=\frac{1}{2}\bigg[\frac{\sqrt{\text{x}.}1-(\text{x}-4).\frac{1}{2\sqrt{\text{x}}}}{\text{x}}\bigg]$
$=\frac{1}{2}\Big[\frac{2\text{x}-\text{x}+4}{2\sqrt{\text{x}.\text{x}}}\Big]$
$=\frac{1}{2}\Bigg[\frac{\text{x}+4}{2(\text{x})^{\frac{3}{2}}}\Bigg]$
$\therefore\text{f}(\text{x})\ \text{x}=1=\frac{1}{2}\Big[\frac{1+4}{2\times1}\Big]$
$=\frac{5}{4}$

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