Question 10 for Quiz

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.