I want to calculate extremes of certain multivariable function $f(x,y)=(6−x−y)x^2y^3$. After solving system of derivatives $f_x=0$ and $f_y=0$ I got something like this:
$P_1=(x,0),x\in \mathbb R$
$P_2=(0,y),y\in \mathbb R$
First two conditions are satisfied with infinite number of $x$ and $y$. How am I supposed to act in such situation? Do I have to check the first two points in some way? If so, how should I do this?