Find a differentiable function that has a minimum in $x^*$

Question

I am studying for an exam and don't have solutions for this exercise:

Let $x^*$ be the unique solution of the linear system of equations $Ax=b$. Formulate a differentiable function, so that this function has its unique minimum in $x^*$.

Answer 1

What about the follwing function:

$f(x):=||Ax-b||^2$

We have $f(x) \ge 0$ for all $x$ and $f(x^*)=0$.

Its your turn to show that $f$ is differentiable.