# Find the maximum and minimum values in a range

I'm trying to understand how to find the minimum & maximum values of this function:

$$f(x,y) = xy-y^2$$

In the following range D:

$$D = \{(x,y) \in R^2 : 0 \leq x \leq 1, |y| \leq x^2 \}$$

Obviously I tried to use Lagranage multipliers, but I was a little confused about the absolute value. Should I divide it to two different equastion systems, one for positive y and one for negative?

Thanks in advance.

## 1 Answer

observe that $$f_x=y$$ and $$f_y=x-2y$$ thus we get the solution $$x=0,y=0$$ from the system $$f_x=0$$ and $$f_y=0$$

• Hey, Lagrange is not required here? it seems too easy the way you showed it :) – superuser123 Jul 14 '16 at 13:17