Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How would I show that the origin of the function $$g(x,y) = x^6 - y^6x^2$$ is a saddle point?

I worked out the Hessian matrix and at $(0,0)$ this matrix is null. Where do I go from here?

share|improve this question
add comment

1 Answer

up vote 2 down vote accepted

$g(x,y)=x^2(x^4-y^6)$ and $g(x,a|x|^{2/3})=x^2(x^4-ax^4)=x^2(1-a)x^4$ for every $a$. You can choose $a<1$ to see that $g$ take positive values in a neighborhood of $(0,0)$, and $a>1$ for negative values.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.