Let f(x,y)=x2y+sin(xy)f(x, y) = x^2y + \sin(xy)f(x,y)=x2y+sin(xy). Find the Hessian matrix HfH_fHf evaluated at (π,0)(\pi, 0)(π,0).
Hf(π,0)=(02π−12π−10)H_f(\pi, 0) = \begin{pmatrix} 0 & 2\pi - 1 \\ 2\pi - 1 & 0 \end{pmatrix}Hf(π,0)=(02π−12π−10)
Hf(π,0)=(02π+12π+10)H_f(\pi, 0) = \begin{pmatrix} 0 & 2\pi + 1 \\ 2\pi + 1 & 0 \end{pmatrix}Hf(π,0)=(02π+12π+10)
Hf(π,0)=(0π2π20)H_f(\pi, 0) = \begin{pmatrix} 0 & \pi^2 \\ \pi^2 & 0 \end{pmatrix}Hf(π,0)=(0π2π20)
Hf(π,0)=(1001)H_f(\pi, 0) = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}Hf(π,0)=(1001)