<Dd> subject to g (x, y) = 0 . </Dd> <P> We assume that both f and g have continuous first partial derivatives . We introduce a new variable (λ) called a Lagrange multiplier and study the Lagrange function (or Lagrangian or Lagrangian expression) defined by </P> <Dl> <Dd> L (x, y, λ) = f (x, y) − λ ⋅ g (x, y), (\ displaystyle (\ mathcal (L)) (x, y, \ lambda) = f (x, y) - \ lambda \ cdot g (x, y),) </Dd> </Dl> <Dd> L (x, y, λ) = f (x, y) − λ ⋅ g (x, y), (\ displaystyle (\ mathcal (L)) (x, y, \ lambda) = f (x, y) - \ lambda \ cdot g (x, y),) </Dd>

Constrained maxima and minima and the method of lagrange multipliers