$4.($Another drill problem$)$ Suppose f $($x$1,$ x$2)=2$x$1$x$2+2$x$1$ x$212$x$22.$ Find all the critical points of f $.$ Determine if each critical point is a maximum, minimum or saddle point. Then simulate using Python the gradient algorithm for computing the minimum. You should write your own gradient algorithm. Try various initial conditions to see how the algorithm performs. $1$