Newton’s method for computing the square root of a positive number. The equation can be written in the form This form leads to Newton’s method: (a) Show that this difference equation has two...

Newton’s method for computing the square root of a positive number. The equation

can be written in the form

This form leads to Newton’s method:

(a) Show that this difference equation has two equilibrium points, − √ b and √ b.

(b) Sketch cobweb diagrams for

(c) What can you conclude from part (b)?

(d) Investigate the case when b = −3 and try to form an explanation of your results.