Question

Let D be the set of all points (x,y) in R^2 such that x is bigger than 0, y bigger than 0 and x+y less than 6. Consider the function f: D --> R defined by
f(x,y) = yx^2(f-x-y)
Determine all points in D where f has a local maximim value and all points in D where f has a local minimum value.

Hint: it may well be that f does not have local maxima or local minima on D, since D is an open domain. The acutal boundary lines of D do not belong to D, and f is not defined there.

Answer 1

assigment attached