Maximize $f(x)=3x_1{x}_2+3x_2{x}_3-x_1^2-6x_2^2-x_3^2.$

Describe how solving this problem can be reduced to solving a two$-$variable unconstrained optimization problem.

Starting from the initial trial solution $(x_1,x_2,x_3)=(1,1,1),$ interactively apply the gradient search procedure with $=0\mathrm{.}05$ to solve $($approximately$)$ the two$-$variable problem identified in part $1.$