Exercice : Let $f :\mathbb R ^2 \to \mathbb R^2$ be the function , defined by : $$ f(x,y)= \begin{bmatrix} x+xy^2 \\ -y+y^2+x^2 \end{bmatrix} $$ How we can compute $D^2f(x_0,y_0)(x,y)$ where $(x_0,y_0)=(0,1)$ ?
I'm confused !! if $D^2f(x_0,y_0)$ is the Hessian matrix of $f: \mathbb R^2 \to \mathbb R^2$, so how we can compute it?
Any help is really appreciated !