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i) We all know that stationary points in 1D are either minima, maxima or inflection points, but consider y=|x|. x=0 is not a stationary point, and yet it is clearly the point at which y is the smallest. Am I technically correct in calling x=0 a 'minimum'? -or should I use some other terminology?

ii) consider y=1/x. In the limit x-> infinity, the derivative dy/dx -> 0. Does that mean that there exists a stationary point in this limit? I know it's an asymptote, but can we speak of a horizontal asymptote as also being a stationary point? (Stationary line?)