Question

Let f(x, y) = ln(1 + x² + y² ) for (x, y) ∈ \(\R^2\). Define
\(\begin{matrix} P=\frac{∂^2f}{∂x^2}|_{(0,0)} &  Q=\frac{∂^2f}{∂x∂y}|_{(0,0)} \\  R=\frac{∂^2f}{∂y∂x}|_{(0,0)} &  S=\frac{∂^2f}{∂y^2}|_{(0,0)} \end{matrix}\)
Then

• A. PS − QR > 0 and P < 0
• B. PS − QR > 0 and P > 0
• C. PS − QR < 0 and P > 0
• D. PS − QR < 0 and P < 0

Answer 1

The Correct Option is B

The correct option is (B) : PS − QR > 0 and P > 0.