The utility function $U=f(x, y)$ is a measure of the utility (or satisfaction) derived by a person from the consumption of two products $x$ and $y .$ Suppose the utility function is
$U=-5 x^{2}+x y-3 y^{2}$
(a) Determine the marginal utility of product $x$.
(b) Determine the marginal utility of product $y$.
(c) When $x=2$ and $y=3$, should a person consume one more unit of product $x$ or one more unit of product $y$ ? Explain your reasoning.
(d) Use a computer algebra system to graph the function. Interpret the marginal utilities of products $x$ and $y$ graphically.