Saddle Point Meaning. A critical point of a function of a single variable is either a local maximum a local minimum or neither. Saddle point definition a point at which a function of two variables has partial derivatives equal to zero but at which the function has neither a maximum nor a minimum value.
A point on a curved surface at which the curvatures in two mutually perpendicular planes are of opposite signs compare anticlastic. Hence the fixed point at the origin is a saddle point. A value of a function of two variables which is a maximum with respect to one and a minimum with respect to the other.
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1 A point at which a curved surface is locally level but at which its curvature in two directions differs in sign ie. Saddle Point A point of a function or surface which is a stationary point but not an extremum. A critical point of a function of a single variable is either a local maximum a local minimum or neither. In other words a point p with f p 0 and the property that for all ϵ 0 there exist two points q 1 and q 2 with p q 1 ϵ p q 2 ϵ and f q 1 f p f q 2.
