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

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Somefantastik
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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} &gt; 0 \ for \ all \ x,y \ in \ R^{2}

V&#039;(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?
 
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Hi Somefantastik! :smile:

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