We have the following multi-variable function f(x,y) = x^{3}-12xy+8y^2 .

We have the following multi-variable function .

(a) Given only this function, let's try to search for all local extremal values of the function and we also have to categorize each extremal value as either a local minima/maxima or saddle point.

(b) Looking at the function, we see that the domain of f is . From this information and from part b, let's find the absolute maximum and minimum values, if they actually exist. If any absolute value(s) does not exist, please explain the reasoning.