If the first derivative of something is $x^TA+b$ and its second derivative is $A^T$ how do I know for which values of $x$ is minimum or maximum? $x$ is a vector and $A$ is a square matrix.
$A$ is invertible and symmetric. The original function $f(x) = \frac12 x^TAx+b^Tx$
The derivative is suppose to be $Ax+b$. Equating to $0$ and solve for $x$ would give us the stationary point.
If $A$ is positive definite, it is a global minimium.
If $A$ is negative definite, it is a global maximum.
Otherwise, it is neither.