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Say for example we have a composite function with this graph.

and we take the shown interval $[a,b]$ , can we say that this graph has a local minimum at the point $x=c$?

Example image

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    $\begingroup$ No, it is an infimum. $\endgroup$ – Yves Daoust Jul 17 '17 at 17:34
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    $\begingroup$ No, it has a local maximum at $c$ – but it is not a maximum on $(a,b)$. $\endgroup$ – Bernard Jul 17 '17 at 17:35
  • $\begingroup$ @Yves Daoust: an infimum??? $\endgroup$ – Bernard Jul 17 '17 at 17:37
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    $\begingroup$ Oh so what you (Bernard) are saying is that since all points near x=c have a lower value than f(c) then it counts as a local maximum ? I can kinda understand that $\endgroup$ – Dahen Jul 17 '17 at 17:40
  • $\begingroup$ An infimum? I don't think I've studied that yet, can you give me a short explanation on what it is? $\endgroup$ – Dahen Jul 17 '17 at 17:41

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