1. The problem statement, all variables and given/known data Given a function f: R^2 -> R of class C^3 with a critical point c. Why CANNOT the hessian matrix of f at point c be given by: 1 -2 2 3 2. Relevant equations 3. The attempt at a solution So first i want to clarify this. When it says f: R^2 -> R, that means the function is of two variables (x and y)? And when it says class C^3 that means the third derivative of the function exists and is continuous. So would a function be x^3 or x^4? the third derivative would be 24x for x^4 and is continuous. The third derivative of x^3 would be 6. I'm not sure about the answer..