Multivariable calculus - Trying to understand if a stationary point is a saddle point, max or min

Question

I have the following function

$f(x, y) = x^4+y^4 $

$(0, 0)$ is a stationary point, so I calculat the determinant of the Hessian Matrix, which is 0, so I try to understand what kind of point that is by finding the eigenvalues of the matrix. I get one which is, again, $0$.

I read that now if I want to understand if it's a saddle point, I can use the Taylor expansion and I'd like to learn more about the Taylor expansion since I read about it everywhere, but I don't know how to start with this function.

Answer 1

Since $(\forall(x,y)\in\mathbb{R}^2):f(x,y)=x^4+y^4\geqslant0=f(0,0)$, $(0,0)$ is a global minimum.