# Math 22 Lagrange Multipliers

## Method of Lagrange Multipliers

 If ${\displaystyle f(x,y)}$ has a maximum or minimum subject to the constraint ${\displaystyle g(x,y)=0}$, then it will occur at one of the critical numbers of the function  defined by
${\displaystyle F(x,y,\lambda )=f(x,y)-\lambda g(x,y)}$.

In this section, we need to set up the system of equations:

${\displaystyle F_{x}(x,y,\lambda )=0}$
${\displaystyle F_{y}(x,y,\lambda )=0}$
${\displaystyle F_{\lambda }(x,y,\lambda )=0}$