How to Find a Region Where V'(x,y) < 0?

[Somefantastik]

Hi,

I've got a function that I'm trying to show is positively invarient.

$$Let \ V(x,y) = 0.45x^{2}+xy+0.56y^{2} > 0 \ for \ all \ x,y \ in \ R^{2}$$

$$V'(x,y) = ... = -8.4840x^{2} - 18.7412x - 10.3496 - 0.011xy - 0.011y^{2};$$

How can I find a neighborhood/region that makes V'(x,y)< 0?

 

[tiny-tim]

Hi Somefantastik!

Complete the square (twice) … write it in the form -A(x - B)² - C(x - D)² +E