 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-2/10/b/solution

The gradient vanishes at the origin. Its Hessian matrix there is

H = (0110),

1

and

- 1

. The quadratic term is therefore indefinite, so the origin is a saddle point of a scalar function. Equivalently, the leading term

x y

is positive along

y = x

and negative along

y = - x

 New to topics? Read the docs here!