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I'm designing a website that teaches Calculus I and am currently working on finding absolute extrema of a function. Here is the question.

Identify the absolute maximums and minimums of $f(x) = \cos(x)$ on the interval $[0,2\pi]$.

It is obvious that $\cos(x)$ has an absolute minimum of $-1$ at $x = \pi$. However, at the endpoints $0$ and $2\pi$, $\cos(x)$ exhibits maximum values of $1$. Can I classify both of these points as absolute maximums?

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    Is there a place in $[0,2\pi]$ where $\cos(x)>1$ ? – 2017-01-15
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    You cannot classify the points at maximums -- only the values. And the value $+1$ is indeed a maximum. The points are the locations at which the maxima occur, and both $0$ and $2\pi$ are such points. But there's another question: should you, not knowing the answer to this question, really be the person designing a website to teach calculus? – 2017-01-15
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    You might want to read through Michael Spivak's "*Calculus*" and be sure you can do most of the problems in it; doing do will help resolve questions like this one for your future work. Best of luck. – 2017-01-15
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    here you can find the plot of this function https://www.wolframalpha.com/input/?i=plot+cos(x)+for+x%3D0+to+2*pi – 2017-01-15

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