The approximate value of `f(x)=x^(3)+5x^(2)-7x+9` at `x=1.1` is

Options

A. 8.6
B. 8.5
C. 8.4
D. 8.3

Answer

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 `DeltaA=0.1` so that
`f(x+Deltax)=f(1+0.1)=f(1.1)`
We know that
`f(x+Deltax)=f(x)+Deltaxf'(x)`
`=x^(3)+5x^(2)-7x+9+Deltax xx (3x^(2)+10x-7)`
Put `x=1` and `Deltax=0.1` we get
`f(1+0.1)=1^(3)+5(1)^(2)-7(1)+9+0.1xx(3xx1^(2)+10xx1-7)`
`impliesf(1.1)=1+5-7+9+0.1(3+10-7)`
`=8+0.1(6)`
`=8+0.6=8.6`