a$.$ Write the first$-$order necessary optimality conditions. Is this condition also

sufficient for optimality? Why?

b$.$ Is x $=(0,0)$t an optimal solution? If not, identify a direction d along which

the function would decrease.

c$.$ Minimize the function starting from $(0,0)$ along the direction d obtained in

Part b$.$

d$.$ Dropping the last term in the objective function, use a classical direct optimization technique to solve this problem.