Hi, I was thinking about the following and would like some clarification. Suppose that we have a continuous scalar function [itex]f:R^n \to R[/itex] with a critical point at say x_0, where the dimension of x_0 depends on the value of n.(adsbygoogle = window.adsbygoogle || []).push({});

Consider as an example f(x) = x (n = 1). The point x = 0 is a critical point since f'(x) is zero at that point. Since f is continuous then corresponding to x = 0 must be a local minimum, local maximum or saddle correct? (Not exactly sure about it)

My point is that x = 0 lies on a line of fixed points and hence cannot correspond to a maximum or a minimum? Is this true in higher dimensions or does this reasoning hold at all?

Any help would be good thanks.

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