I have to solve the following problems without using derivatives.
Does $ f(x,y) = x^6-3x^2y-6x+5y $ have a maximizer or minimizer?
My attempt: Since $ x^6 $ and $ y^2 $ are squares, if we can write $ -3x^2y-6x+5y $ can be written as a square then we can coclude whether the function is a maximizer or minimizer.
Does $ f(x,y) = (x^6+7y^3+4)e^{-x^2-y^2} $
My attempt: If $ x^6+7y^3+4 $ can be written as a sum of squares then we can deduce whether maximizer or minimizer.
Would appreciate if if someone could direct me in the correct path or give me some hints.