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If we the function $f(x)$ in the interval $x \in [\frac{\pi}{4}, \frac{7\pi}{4}]$, will $\frac{\pi}{4}$ be one of the local minima and $\frac{7\pi}{4}$ one of the local maxima?

Also if the interval was $x \in (\frac{\pi}{4}, \frac{7\pi}{4})$, will the number just little more than $\frac{\pi}{4}$ be one of the local minima and number just little less than $\frac{7\pi}{4}$ one of the local maxima? If yes, is there anyway to denote that number using limits or something?

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    Try your first question on the function $f(x)=-x$.2012-08-05
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    Then try it on $f(x)=\sin x$.2012-08-05
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    And there is no such thing as "the number just little more than $\pi/4$".2012-08-05

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