Question

If the Hessian matrix of a function is zero then the critical point is?

(a) It cannot be concluded

(b) Always at Origin

(c) Depends on Function

(d) (100,100)

I have been asked this question in an interview.

I would like to ask this question from Maxima and Minima of Two Variables topic in section Maxima and Minima of Engineering Mathematics

Answer 1

Right answer is (a) It cannot be concluded

For explanation: If the Hessian matrix is zero then the second derivative test fails and nothing can be said about the critical points.