Using differentiation, approximate value of f(x)=x^2-2 x+1 at x=2… - Vidyadip

MCQ

Using differentiation, approximate value of $f(x)=x^2-2 x+1$ at $x=2.99$ is

✓
3.96
B
9.96
C
4.98
D
5.98

✓

Answer

Correct option: A.

3.96

(a): We have, $f(x)=x^2-2 x+1$
$
\Rightarrow f^{\prime}(x)=2 x-2
$
Now, $a+h=2.99=3+(-0.01)$, where $a=3$ and $h=-0.01$
We know that, $f(a+h) \approx f(a)+h f^{\prime}(a)$
$
\begin{aligned}
\Rightarrow & f(2.99) \approx f(3)-0.01 f^{\prime}(3)=(9-6+1)-0.01(6-2) \\
& =4-0.04=3.96
\end{aligned}
$

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