What are the critical points, if any, of #f(x,y) = 5x^2 + 4xy + 3y^2 - 52x - 56y + 13#?
We will determine the stationary points instead. Those points observe the condition
In the present case we have
and for stationary points determination
Point qualification is obtained by computing
In this point we have
This matrix is positive definite because it have two positive eigenvalues