D$.$I.C $13\mathrm{.}5-3."$ Starting from the initial trial solution $(x_1,x_2)=(0,0),$ interactively apply the gradient search procedure with $lon=0\mathrm{.}3$ to obtain an approximate solution for the following problem, and then apply the automatic routine for this procedure $($with $lon=0\mathrm{.}01).$

Maximize $,f(x)=8x_1-x_1^2-12x_2-2x_2^2+2x_1{x}_2.$

Then solve gradf$(x)=0$ directly to obtain the exact solution.

$13\mathrm{.}5-5.$ Starting from the initial trial solution $(x_1,x_2)=(0,0),$ apply one iteration of the gradient search procedure to the following problem by hand:

Maximize $,f(x)=4x_1+2x_2+x_1^2-x_1^4-2x_1{x}_2-x_2^2.$

To complete this iteration, approximately solve for $t^{**}$ by manually applying two iterations of the bisection method with initial bounds $t=0,i=1.$

Please solve this questions below without ai and step by step.