Show at least two iterations manually for each problem before running the MATLAB$/$python code to give the answer.

Minimize the function $f(x_1,x_2)=x_1^2+4x_2^2-4x_1{x}_2+2x_1$ starting from the initial guess $x^{(0)}=\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$

By doing the following steps

a$)$ Compute the gradient and Hessian

b$)$ Form the Trust$-$Region subproblem

c$)$ Compute the dog$-$leg step

d$)$ Test the step by calculating the actual reduction and the predicted reduction and either accept or reject the step, then update the trust region radius accordingly until you attain convergence $($i$.$e$.||gradf(x)||$ is small enough$)$