This problem considers solving ( ) = 0, where                                 (a) Sketch ( ) for 0 ≤  ≤ 2 . How many solutions of ( ) = 0 are there in this interval? (b) Using Newton’s method, take 0...

This problem considers solving
() = 0, where

(a) Sketch
() for 0 ≤
 ≤ 2. How many solutions of
() = 0 are there in this interval?

(b) Using Newton’s method, take

₀
= 2/3 and calculate

₁
(by hand). After this, calculate

₂
(by hand).

(c) Sketch the tangent lines for

₀
and

₁. Based on this, determine what the others


_i

values will be.

(d) Explain why Newton’s method will not converge for this problem.