$4.$ Consider the following optimization problem.

Maximize f$($x$)=$ x$1$x$2+3$x$2-$ x$1^2-$x$2^2$

a$.$ Show that this problem satisfies the assumptions necessary for applying the gradient

search procedure. $($Hint: what does a Hessian tell us$?)$

b$.$ Starting from the initial trial solution $($x$1,$ x$2)=(0,0),$ apply two iterations of gradient

search