saddle point
saddle pointA point at which a function of two variables takes a maximum for movement in some directions and a minimum for movement in other directions. The term is borrowed from geography, where a saddle is a low point in a range of hills. For example, if y = x2 − z2, ∂y/∂x = 2x and ∂2y/∂x2 = 2; thus if x is varied holding z constant, y has a minimum at x = 0. But ∂y/∂z = −2z and ∂2y/∂z2 = −2; thus if z is varied holding x constant, y takes a maximum at z = 0. The origin is therefore a saddle point for this function. The directions in which movement is considered need not correspond to the axes. Consider for example...
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