GATE 2026 MN – Question 36
For $f(x,y)=x^2+y^2+xy-8x-7y$, find the determinant of the Hessian at its stationary point.
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Correct answer: (B) 3
Explanation
Second derivatives are fxx=2,fyy=2 and fxy=fyx=1. Therefore the Hessian is the constant matrix[[2,1],[1,2]], with determinant4−1=3, B. Its value does not require first locating the stationary point.