Consider the following unconstrained optimization problem:

maxf$(x)=2x_1{x}_2+x_2-x_1^2-2x_2^2$

a$)$ Starting from the initial trial solution $(x_1,x_2)=(1,1),$ interactively apply the gradient

search procedure with $=0\mathrm{.}25$ to obtain an approximate solution.

b$)$ Solve the system of linear equations obtained by setting gradf$(x)=0$ to obtain the exact

solution.