I am trying to calculate stationary point x* by calculating the first derivative of function $f(x) = c^T x +1/2 x^T Hx$ and find out whether it is a minimizer of f. I wrote the part with $c^T x$, also I am not sure about that, too. Could you please help me about writing second part with $1/2 x^T Hx $ ?
c=\begin{bmatrix} 1 \\3 \\-7 \\1 \\\end{bmatrix} H=\begin{bmatrix}4 & 4 & 4 & 3 \\4 & 7 & 3 & 3 \\4 & 3 & 5 & 3 \\3 & 3 & 3 & 3 \\ \end{bmatrix} $c^T x$ = $x_{1} + 3x_{2} -7x_{3} + x_{4}$