6.7. Consider the function f: R² → R defined by f(x, y) = 2x³-3x²-6xy(x − y − 1). - (a) Determine all of the critical points of f ana- lytically (i.e., without using a computer). (b) Classify each critical point found in part a as a minimum, a maximum, or a saddle point, again working analytically. (c) Verify your analysis graphically by creating a contour plot or three-dimensional surface plot of f over the region -2< x <2, -2≤ y ≤2. (d) Use a library routine for minimization to find the minima of both f and -f. Experiment with various starting points to see how well the routine gets around other types of critical points to find minima and maxima. You may find it instructive to plot the sequence of iterates generated by the routine.