Problem $2$: Write a MATLAB script called hw$4\_$p$2$a$.$m to use the gradient$-$descent method to

minimize $f(x)=30x_1^2+30x_2^2.$ Then write a MATLAB script called hw$4\_$p$2$b$.$m to

minimize $f(x)=30x_1^2+x_2^2.$ For each script, use $x^{(0)}=[420,68{]}^T$ as the starting point

and as the stopping criterion.

Notation note: $x^{(0)}$ denotes the initial $x$ vector $($bold to denote vector; $0$ to denote

iteration number$).$ Do not confuse this with $x_i($a scalar$),$ which denotes an individual

component $($the $i^{th}$ one$)$ of the vector, $x.$

Discuss your results: Why did the algorithm work better for one function and worse

for the other?

Hint: We talked about it in class.

$5$ bonus points: Plot the trajectories of your iterates in the $x_1-x_2$ plane $($with lines

and line markers$).$