1. Suppose $g: \mathbb{R}^3 \rightarrow \mathbb{R}$ and
$g(1, 2, 3) = 4$ $\nabla g(1, 2, 3) = (1, 3, 4)$ $H_g(1, 2, 3) = \begin{pmatrix} \frac{1}{\pi} & \frac{\pi}{\ln(7)} & A\\0 & B & -\frac{\sqrt{3}}{2} \end{pmatrix}$
(a) What must A and B equal for the matrix $H_g$ to be the Hessian matrix of g?
(b) What is the second order Taylor approximation for g at (1, 2, 3)? Express the polynomial $T_2$ in terms of $(h_1, h_2, h_3)$.