![image](https://tex.z-dn.net/?f=z%3Dxy%5E2-xy-xy%5E3%5C%5C+z%27_x%3Dy%5E2-y-y%5E3%3Dy%28y-1-y%5E2%29%5C%5C+z%27_y%3D2xy-x-3xy%5E2%3Dx%282y-1-3y%5E2%29%5C%5C+%5Cbegin%7Bcases%7D+y%28y-1-y%5E2%29%3D0%2C+%5C%5C+x%282y-1-3y%5E2%29%3D0%2C+%5C%5C+x%3E0%2C+%5C%5C+y%3E0.+%5Cend%7Bcases%7D%5C%5C)
0, \\ y>0. \end{cases}\\" alt="z=xy^2-xy-xy^3\\ z'_x=y^2-y-y^3=y(y-1-y^2)\\ z'_y=2xy-x-3xy^2=x(2y-1-3y^2)\\ \begin{cases} y(y-1-y^2)=0, \\ x(2y-1-3y^2)=0, \\ x>0, \\ y>0. \end{cases}\\" align="absmiddle" class="latex-formula">Система имеет беск много решений, экстремумов нет