Applications of Derivatives — Maths STD 12 Science — Question

Let $f ( x )=\sqrt{x}$.
Then $f^{\prime}(x)=\frac{1}{2 \sqrt{x}}$.c
Take a = 9 and h = – 0.05.
Then $f(a)=f(9)=\sqrt{9}=3$ and
$f^{\prime}(a)=f^{\prime}(9)=\frac{1}{2 \sqrt{9}}=\frac{1}{6}$.
The formula for approximation is
$f(a+h) \doteqdot f(a)+h . f^{\prime}(a)$
$\therefore \sqrt{8.95}= f (9-0.05)$
$\doteqdot f(9)-(0.05) f^{\prime}(9)$
$\doteqdot 3-0.05 \times \frac{1}{6}$
$\doteqdot 3-0.0083=2.9917$
$\therefore \sqrt{8.95} \doteqdot 2.9917$.