So I have this function
$ f(x,y) = x^4 - 2x^2 +x + 4y^2 $
and I want to know if the steepest gradient method will converge if I pick an arbitrary point and apply said method.
My initial thought was to find the Hessian and check if greater than 0, because if so I know this converges to a global optimum but I get
$$ \begin{bmatrix} 12x^2 - 4 & 0 &\\ 0 & 8 &\\ \end{bmatrix} $$
and I'm not sure what to do next.
How should I go about finding whether the steepest gradient method will converge?