# Tangent plane

### From Glossary

Consider the surface,
where
A *differentiable curve* passing thru
is
for which the derivative, exists, where The *tangent plane* at is the set of all initial derivatives: (This is a misnomer, except in the special case of one function and two variables at a non-stationary point.) An important fact that underlies the classical Lagrange multiplier theorem when the rank of
is full row ( is then called a *regular point*): the tangent plane is

Extending this to allow inequalities, the equivalent of the tangent plane for a regular point is the set of directions that satisfy first-order conditions to be feasible: