Given $f(x) = \frac{1}{2}x^TAx + b^Tx + \alpha $
where A is an nxn symmetric matrix, b is an n-dimensional vector, and alpha a scalar. Show that
$\bigtriangledown _{x}f(x) = Ax + b$
and
$H = \bigtriangledown ^{2}_{x}f(x) = A$
Is this simply a matter of taking a derivative with respect to X, how would you attack this one?