Hello Everyone, In class, I am given to show that maximizing over x1 first and then maximizing over x2 for f(x1,x2) is the same as maximizing x2 first and then maximizing over x1 for f(x1,x2), assuming f(x1,x2) is always continuous. Graphically, this statement is apparent to me, because maximizing over x1 first for f(x1,x2) means to find a… Show more

The definition of a critical point is where both the partial derivatives (wrt x and wrt y) equal 0. You cannot take the derivatives separately. If you have a radially symmetric surface, you will luck out and be ok, but for something lacking that symmetry, you most likely not find any maximum, let alone a global max. For instance, plot up f(x,y)…