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What is the definition of a "turning point"?

For example, here's a definition that I feel doubtful about:

• The Concise Oxford Dictionary of Mathematics

  Some authors use `turning point' as equivalent to stationary point

(I get the feeling that this term is not really used by mathematicians and mostly used only in middle- and high-school math. Moreover, it is not usually given any precise definition. Is my feeling correct?)

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1 Answer

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Generally, you can view a "turning point" as a point where the curve "changes direction": for example, from increasing to decreasing or from decreasing to increasing. You can visualise this from the following graph, try following the graph as it goes up then down then up.

It then follows that "turning points" are either maximum or minimum points and are stationary. However, stationary points are not always turning points, see stationary points of inflexion like the one below:

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