Teaching JKPSC Lecturership Mock Test Series 2024-25 Mathematical Science Analysis Functions of Several Variables
Let f(x, y) = ln(1 + x2 + y2) for (x, y) ∈ ℝ2. Define
\(P=\left.\frac{\partial^2 f}{\partial x^2}\right|_{(0,0)} \)
\(Q=\left.\frac{\partial^2 f}{\partial x \partial y}\right|_{(0,0)} \)
\(R=\left.\frac{\partial^2 f}{\partial y \partial x}\right|_{(0,0)} \)
\(S=\left.\frac{\partial^2 f}{\partial y^2}\right|_{(0,0)}\)
Then
1
PS − QR > 0 and P < 0
2
PS − QR > 0 and P > 0
3
PS − QR < 0 and P > 0
4
PS − QR < 0 and P < 0