Method of Lagrange

We use the Method of Lagrange to find extremums of multivariate functions with respect to a constraint. To do so, we first find its critical point (with respect to a constraint), and afterwards, evaluating those points using , we conclude

  • Biggest values = global max
  • smallest values = global min


To find the critical points of subject to a constraint where ( is a constant), find the values of and for which

is known as the Lagrange Multiplier.





For inequalities, find critical points of , then only consider the points inside the boundary condition.

Then, use lagrange to check at the edge of the boundary.