Question

define saddle point in partial differential equations
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Answer 1

Step-by-step explanation:

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 {\displaystyle f(x,y)=x^{2}+y^{3}}{\displaystyle f(x,y)=x^{2}+y^{3}} has a critical point at {\displaystyle (0,0)}(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 {\displaystyle y}y-direction.