<P> In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) of orthogonal function components defining the surface become zero (a stationary point) but are not a local extremum on both axes . The saddle point will always occur at a relative minimum along one axial direction (between peaks) and at a relative maximum along the crossing axis . </P> <P> The name derives from the fact that the prototypical example in two dimensions is a surface that curves up in one direction, and curves down in a different direction, resembling a riding saddle or a mountain pass between two peaks forming a landform saddle . In terms of contour lines, a saddle point in two dimensions gives rise to a contour graph or trace that appears to intersect itself--such conceptually might form a' figure eight' around both peaks; assuming the contour graph is at the very' specific altitude' of the saddle point in three dimensions . </P>

The what is the extreme point on half of a hyperbola