please solve part c by hand $....$ Consider the function

$f(x,y)=x^2+\frac{1}{2}{y}^2-xy+x-2$

and a starting point $(0,0{)}^{TT}.$

$($a$)$ Find all local minima and local maxima analytically $($i$.$e$.$ using necessary and sufficient conditions$).$

$($b$)$ Is $d=(-1,3{)}^{TT}$ a descend direction for $f$ at $(0,0{)}^{TT}?$

$($c$)$ Perform $2$ steps of gradient descent with constant step size $=\frac{1}{2}.$ You can solve this problem

by hand $($display all intermediate steps$)$ or write a program for the method $($you can use any

programming language; display all intermediate steps and attach your code$).$