 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-2/19/a/i/solution

f_{xx} = 4

f_{x y} = f_{y x} = 3 + 2 y

and

f_{yy} = 2 + 2 x + 30 y

. Evaluating at the origin gives the Hessian matrix

H_{f} (0, 0) = (4332) .

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