This exercise considers Newton’s method and the finite termination property. The equation to solve is ( ) = 0, where ( ) = ( 2 − 1). (a) Sketch ( ) and locate the three solutions. (b) Suppose Newton’s...

This exercise considers Newton’s method and the finite termination property. The equation to solve is
() = 0, where
() =
(
²
− 1).

(a) Sketch
() and locate the three solutions.

(b) Suppose Newton’s method is to be used to locate the solution
 = 1. What does

₀
need to be so the problem is solved exactly in one step? Assume here that

₀
 1.

(c) Using your sketch in part (a), and the result from part (b), explain where

₀
should be located (approximately) so the solution
 = 1 is found in exactly two steps.