The approximate value of $f(x)=3 x^{2}+5 x+3$ at $x=3 \cdot 02$ is
The approximate value of $f(x)=3 x^{2}+5 x+3$ at $x=3 \cdot 02$ is
- $45.46$
- $45 \cdot 46$
- $44 \cdot 76$
- $44 \cdot 46$
Solution
Given $f(x)=3 x^{2}+5 x+3 \Rightarrow f^{\prime}(x)=6 x+5$
Let $\mathrm{a}=3, \mathrm{~h}=0.02$
$\therefore \mathrm{f}(\mathrm{a}) \quad=\mathrm{f}(3)=27+15+3=45$
$f^{\prime}(a)=f^{\prime}(3) \quad=18+5=23$
We know that
$\begin{aligned}
\mathrm{f}(\mathrm{a}+\mathrm{h}) & \div \mathrm{f}(\mathrm{a})+\mathrm{hf}^{\prime}(\mathrm{a}) \\
&=45+(0.02)(23)=45+0.46=45.46
\end{aligned}$
Asked in: MHT CET 2020 (20 Oct Shift 1)
Practice more Applications of Derivatives questions on Aicharya