Imagine we want to maximize or minimize a two-variable function f (x, y) subject to the constraint g(x, y)

Imagine we want to maximize or minimize a two-variable function f (x, y) subject to the constraint y) O. In this case the maxima and minima must either occur at Lagrange points on the boundary (i.e. g(x, y) = O) or at critical points of f in the interior (i.e. g(x, y) < O). Now imagine we want to maximize or minimize a three-variable function f (x, y, z) subject to the two con- straints y, z) = O and h(x, y, z) = O. In this case we form the five-variable function As in the single constraint case, the maxima and minima must correspond to points where all five partial derivatives are zero.