$28.$ Consider a quadratic function $$: $2->,=$

$1$

$2$

$$

$+$

$,$ where

$=[$

$1$

$2$

$],=[$

$21$

$120],=[$

$5$

$3$

$]$

$1)$ Find the minimal value of f$,$ and the corresponding x$,$ in an analytical way $($i$.$e$.,$ solution in

a closed form$).$

$2)$ Write a program to search for the minimum point of f using gradient descent algorithm

with a constant step$-$size.

$3)$ Write a program to search for the minimum point of f using gradient descent algorithm

with a line search for step$-$size.

$4)$ Write a program to search for the minimum point f using Newton method algorithm.

$5)$ Compare the above results