(10 points) Consider the function described by the following graph. We wish to estimate the value of the root r, labelled in the diagram, using Newton's method. Your diagrams do not need to be perfect but try to copy the given graph and its important characteristics.
i) (4 points) Using a diagram, indicate x_(2) if you start Newton's method with x_(1)=1.
ii) (4 points) Using a diagram, indicate x_(2) if you start Newton's method with x_(1)=3.
iii) (2 points) Which is a better choice of x_(1),1 or 3 ?
2. (10 points) Consider the function described by the following graph. We wish to estimate the value of the root r, labelled in the diagram, using Newton's method. Your diagrams do not need to be perfect but try to copy the given graph and its important characteristics.
y=f(
4
i(4 points Using a diagram, indicate if you start Newton's method with =1. ii) (4 points) Using a diagram, indicate if you start Newton's method with x1 =3. iii)2 points) Which is a better choice of 1,1 or 3