In mathematics, a saddle point or minimax point[1] is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function.[2] An example of a saddle point is when there is a critical point with a relative minimum along one axial direction (between peaks) and at a relative maximum along the crossing axis. However, a saddle point need not be in this form. For example, the function f ( x , y ) = x 2 + y 3 {\displaystyle f(x,y)=x^{2}+y^{3}} has a critical point at ( 0 , 0 ) {\displaystyle (0,0)} that is a saddle point since it is neither a relative maximum nor relative minimum, but it does not have a relative maximum or relative minimum in the y {\displaystyle y} -direction.