# Global Extremum – Domain of ellipse – Exercise 4749

Exercise

Find the maximum value and the minimum value of the function

$$z(x,y)=x-2y$$

In the domain:

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

$$\max_D z(2,-1) = 4,\min_D z(-2,1) =-4$$