This problem explores when Newton’s method converges either faster or slower than stated in Theorem 2.2. (a) Suppose  Show that XXXXXXXXXXis replaced with                                 Where...

This problem explores when Newton’s method converges either faster or slower than stated in Theorem 2.2.

(a) Suppose
 Show that (2.19) is replaced with

Where
 Explain why, in this case, Newton’s method is third-order.

(b) Suppose the assumption that
 is replaced with
 Show that (2.19) is replaced with

Explain why, in this case, Newton’s method is first-order.