How to prove that the following function is non-convex?
$$f(\mathbf{c}) = \left( \|\mathbf{V}\|_{2}^2 - \|\mathbf{A}\cdot\mathbf{c}\|_{2}^2 \right)^2$$
I am trying to do it by demonstrating that $f$ does not fulfil
$$f(\alpha x+\beta y) \leq \alpha f(x)+\beta f(y)$$
with the help of the triangle inequality. Unfortunately, I am stuck since hours in an endless loop of confusing computations that I can't manage to solve. Does anyone have any hints or shortcuts for a reasoning showing that $f$ is not convex?
Thank you in advance for any help.