Answer:
Option A
Explanation:
Given, $f(x) = x^{3}+5x^{2}-7x+9$
On differentiating both sides w.r.t x , we get
f'(x) = $3x^{2}+10x-7$
Let x=1 and $\triangle x$=0.1 , so that
$f(x+\triangle x)=f(1+0.1)=f(1.1)$
We know that ,
$f(x+\triangle x)=f(x)+\triangle x f'(x)$
= $x^{3}+5x^{2}-7x+9+\triangle x\times (3x^{2}+10x-7)$
Put x=1 and $\triangle x$=0.1 , we get
f(1+0.1)
= $1^{3}+5(1)^{2}-7(1)+9+0.1\times (3\times 1^{2}+10\times1-7)$
$\Rightarrow$ $ f(1.1)=1+5-7+9+0.1(3+10-7)=8+0.1(6)=8+0.6=8.6$
