The question presents itself with a function f(x, y) with

- the gradient vector \nabla f(x_0, y_0) = (0, 0), and
- the Hessian of H(x_0, y_0) = \begin{bmatrix}
2 & 0 \\
0 & 10 \\
\end{bmatrix}

Am I missing out something about the gradient vector and Hessian? It seems impossible to derive the second derivatives other than 0 from our gradient vector of (0,0)?

Dear @Khong_Jia_Ren I think I have not fully understood your question. Please elaborate your question more.

However, I think this fact would probably help you with your question that **∇f(x0,y0)=(0,0)** simply means that the first derivates of the function (which is not explicitly given here) at points *x0* and *y0* are equal to *(0, 0)*. In other words, if you have the first derivatives, and you plug in two arbitrary values of *x0* and *y0*, the resulting point would be *(0, 0)*. Now, if we go further and derive it once more, we get the Hessian matrix in question.

Hope this answer helps you out.