Newton's method for unconstrained minimization

Question

Let $f(x) = \frac{1}{2} x^T Q x + b^T x + c.$ Prove that Newton's method finds a critical point after a single iteration.

Here $Q$ is positive definite. For this:

I need to find first of

$\nabla f(x) = $

$\nabla^2 f(x) = $

I am confused about how do I get gradient of this function. Once I know the gradient, I think I can do it. Any help would be appreciated

Answer 1

$\nabla f(x) = \frac 1 2 (Q^T+Q)x + b$ and $\nabla^2 f(x) = \frac 1 2 (Q^T + Q)$