Lagrange multipliers

To optimize a function $f(x,y)$ subject to a constraint $g(x,y)=c$, the gradients must be parallel at an extremum: $
abla f=\lambda\nabla g$.Solvethisvectorequationtogetherwiththeconstraintequationfor$x$,$y$,and$\lambda$.Eachsolutionpointisacandidate;evaluate$f$ at all candidates to identify the maximum and minimum values.