Math 22 Lagrange Multipliers

Method of Lagrange Multipliers

 If $f(x,y)$ has a maximum or minimum subject to the constraint $g(x,y)=0$, then it will occur at one of the critical numbers of the function  defined by
 $F(x,y,\lambda )=f(x,y)-\lambda g(x,y)$.
 
 In this section, we need to set up the system of equations:
 
 $F_{x}(x,y,\lambda )=0$
 $F_{y}(x,y,\lambda )=0$
 $F_{\lambda }(x,y,\lambda )=0$
 
 

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