- #1

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Also, if the function has only one stationary minimum point does that mean that that point is its global minimum?

Can someone please confirm these for me

Thank you

- Thread starter ahamdiheme
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- #1

- 26

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Also, if the function has only one stationary minimum point does that mean that that point is its global minimum?

Can someone please confirm these for me

Thank you

- #2

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Not necessarily. Consider the function f, whose graph is the union over all even integers n of the functions f_n(x) = (x + n)^2 each defined over the interval [n-1, n+1]. All of f's stationary points are minimum points, but f is not convex on [n, n + 2] for even n. Perhaps you mean critical points instead of stationary points?If the stationary points of a function are minimum points does that qualify the function to be a convex function?

- #3

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If "stationary minimum" is the same as "local minimum", then not necessarily.Also, if the function has only one stationary minimum point does that mean that that point is its global minimum?

Thank you

Look at the graph of [itex]-x^4 + x^2[/tex]. You can see that it has only one local minimum at x=0, but it's global minimum is at ±∞.

- #4

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Considering the shape of the graph, that makes it convex right?

- #5

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http://en.wikipedia.org/wiki/Second_derivative_test

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