A saddle point is a point at which the partial derivatives of a function are zero (or the tangent plane has a slope of zero) but is not an extremum. Saddle points exist anywhere the determinant of the Hessian matrix is negative (see extreme value#Multivariable functions for more information). File:Helicoid.svg This multivariable calculus-related article contains minimal information concerning its topic. You can help the Mathematics Wikia by adding to it.