What are the extrema and saddle points of #f(x, y) = x^2 + y^2+27xy+9x+3y#?
A saddle point is located at
The stationary poins are determined solving for
obtaining the result
The qualification of this stationary point is done after observing the roots from the charasteristic polynomial associated to its Hessian matrix.
The Hessian matrix is obtained doing
with charasteristic polynomial