(微積分)拉格朗日乘數法(method of Lagrange multipliers)

 有一$f(x,y)$，在$g(x,y)=0$條件底下求極值:

${\frak L}(x,y,\lambda)=f(x,y)+\lambda\cdot g(x,y)$

$$令\left\{ \begin{array}{l}  \cfrac{\partial{\frak L}}{\partial x}=0 \\ \cfrac{\partial{\frak L}}{\partial y}=0 \\  \cfrac{\partial{\frak L}}{\partial \lambda}=0 \end{array}\right. $$

$(x,y) 為極值$