Mainly 1 and 2. 3 and 4 require a matlab code. Bonus if possible

(2) Fixed Point Iteration Method Goal: Find root of f(x)=x35x2+4=(x1)(x24x4) (Remark: roots are 1 and 222 ) (i) Using algebraic manipulation, show that any fixed points of the functions g1(x)=5x4 and g2(x)=x25x4 are roots of f. (ii) Perform three iterations ("by hand") of the fixed point iteration method using g1 and g2 with initial guess p0=2. Do your calculations with 6 decimal digits. (iii) Use Fixed Point Iteration Method (code algo_22_FixedPointIterationMethod.m) with g1, tolerance =106 for the initial values p0=1 and p0=3. Write down the final result and iteration number. Which roots can be obtained? (iv) Use Fixed Point Iteration Method (code algo_22_FixedPointIterationMethod.m) with g2, tolerance =106 for the initial values p0=1 and p0=3. Write down the final result and iteration number. NUS) Explain why the function g2 cannot be used to approximate the root 222