Consider the function **
g (x) = 12x + 4 - cos x.** Given **
g (x) = 0** has a unique solution **
x = b in the interval (−1/2, 0)**, and you can use this
without justification.

(a) Show that Newton's method of starting point **
x _{0}
= 0** gives a number sequence with

**b <··· <x**

_{n+1}<x_{n}<··· <x_{1}<x_{0}= 0(The word "curvature" should be included in the argument!)

(b) Calculate

**x**. Use theorem 2 in section 4.2 (page 229-

_{1}and x_{2}**Error bounds for Newtons Method**) or

**intermediate value theorem**to show that

**x**.

_{2}- b <0.0000003(c) Find a suitable function that you can perform fix piont iteration to find

**b.**Calculate and compare the results of calculating the first three iterations of Newton's method and fix point iteration