3. (18 marks) CO-3: Answer any two from Questions-(3a-3c). Marks break down are as stated. (a) Consider the function, f(x)=x34x2+6. i. (3 marks) Compute any two fixed point functions, g1(x) and g2(x), from the given function f(x). ii. (3 marks) For g1(x) evaluate the convergence rate and determine to which root it is converging to or divergent. iii. (3 marks) For g2(x) evaluate the convergence rate and determine to which root it is converging to or divergent. (b) Consider a set of four data points: f(0)=3,f(4)=2,f(1)=2,f(1)=1. In the following, you are asked to find the best fit polynomial of degree 2 by using the Discrete-square approximation method as follows: i. (3 marks) From the given data, write down the matrices A,b and x. ii. ( 3 marks) Evaluate ATA and det(ATA). iii. (3 marks) Compute the best-fit polynomial of degree 2 . (c) A function is given by f(x)=e0.5x+sinx which is to be integrated on the interval [0,2]. i. (2 marks) Evaluate the exact integral I(f). ii. (3 marks) Compute the numerical integral by using the Newton-Cotes formula with n=2. iii. (4 marks) Also evaluate the numerical integral C1,4 by using the Composite Newton-Cotes formula