Using differentiation, approximate value of `f(x)=x^(2)-2x1` at x=2.99 is . . .

Options

A. 3.96
B. 9.96
C. 4.98
D. 5.98

Answer

A

Explanation

Given function, `f(x) = x^(2) - 2x + 1`
`implies f'(x) = 2x - 2`
Let X = 3 and `Delta x = - 0.01`
So that `f(x + Delta x) = f (2.99)`
We know that, `f(x + Delta X) ~~ f(x) + Delta xf' (x)`
`~~ (x^(2) - 2x + 1) + (0.01) (2x - 2)`
Putting x = 3 and `Delta x = - 0.001` we get
`f(2.00) ~~ (3^(2) - 2 xx 3 + 1) + (0.01) (2 xx 3 - 2)`
`~~ (4) + (-0.01) (4)`
`~~ 4 - 0.004 ~~ 3.96`