Let $Q$ be an $n×n$ symmetric positive definite matrix, $a,b \in \mathbb{R^n}$, and $c \in \mathbb{R}$. Assume all $a_i$, all $b_j$, and $c$ are positive. Also note that $x \geq 0$ means $x_i \geq 0$ for all $i$. Minimize $\frac{1}{2}x^TQx-b^Tx$ subject to $a^Tx \leq c, x > 0$.
Find the candidate(s) for minimizers using the $1^{st}$ order conditions and check whether they satisfy the $2^{nd}$ order conditions.
I know how to work with minimization problems and inequalities given functions but I'm not sure how to determine the $1^{st}$ and $2^{nd}$ order conditions for the above question