The extremum (maximum or minimum) of a scalar objective function f(x) subject to a constraint g(x) = 0 satisfies all of the following conditions, EXCEPT: 1) the normal to the constraint set is perpendicular to the contour lines of the objective function. 2) the tangent of the constraint set is parallel to the contour lines of the objective function. 3) the normal to the constraint set is perpendicular to the gradient of the objective function. 4) the tangent of the constraint set is perpendicular to the gradient of the objective function.