Question

Question #b399e

Answer 1

`x_3 approx 1.5215`

Explanation:

You are on the right track!

Let `f(x)=2x^(-1)-x^2+1 Rightarrow f'(x)=-2x^(-2)-2x`

`x_1=2`

`x_2=x_1-f(x_1)/(f'(x_1))=2-f(2)/(f'(2))=14/9`

`x_3=x_2-f(x_2)/(f'(x_2))=14/9-f(14/9)/(f'(14/9)) approx 1.5215`