# Global Extremum – Domain of a parabola and a line – Exercise 3463

Exercise

Find the maximum value and the minimum value of the function

$$z(x,y)=2x^3+4x^2+y^2-2xy$$

In the domain

$$D=\{ (x,y): y\geq x^2, y\leq 4\}$$

$$\max_D z(\pm 2,4) = 32,\min_D z(0,0) =0$$