Okay, so I've never seen a question like this before no similar examples in my notes or from past assignments or anything, so I'm literally stumped. The question goes...

*Let $\displaystyle f$ be the function defined by*

$\displaystyle f(x,y)=\alpha+(v_1, v_2) $ $\displaystyle \left( \begin{array}{c} x \\ y \end{array} \right)$ $\displaystyle +(x,y)\left( \begin{array}{cc} a & b \\ b & d \end{array} \right) \left( \begin{array}{c} x \\ y \end{array} \right)$

*where $\displaystyle \alpha, v_1, v_2, a, b, d$ are all real numbers.*

**a) **Compute $\displaystyle \frac{\partial f}{\partial x}$ and $\displaystyle \frac{\partial f}{\partial y}$.

*For what values $\displaystyle v_1$ and $\displaystyle v_2$ is $\displaystyle (0,0)$ a critical point of $\displaystyle f$?*

**b) **Compute $\displaystyle \frac{\partial^2f}{\partial x^2}, \frac{\partial^2f}{\partial x\partial y}, \frac{\partial^2f}{\partial y^2}$

*For what values of $\displaystyle v_1, v_2, a, b, d$ is $\displaystyle (0,0)$ a saddle point of $\displaystyle f$?*