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Numerade Educator

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Problem 33 Hard Difficulty

For what values of $ x $ does the graph of $ f $ have a horizontal tangent?
$ f(x) = x + 2 \sin x $

Answer

$$(2 n+1) \pi \pm \frac{\pi}{3}, n \text { an integer. }$$

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Video Transcript

Hey, it's clear sailing you right here. So we have F of X is equal to X plus to sign, so my first derivatives get one plus to co sign. We know that has a horizontal tangent when the first derivative it's equal to zero. So it's worn plus to co sign is equal to zero. So we get X is equal to two pi thirds or four pi thirds. We put it in the form Texas difficult to two pi over three was two n pi since co sign has a period of two pi Or it could be xs equal to four pipe thirds plus two and pie and is any integer. You realize that these solutions to pie throwers and four pi thirds rpai plus or minus pi over three. So to be written, there's two and prying was pie, plus or minus pi thirds just equal to two end plus one times pi plus or minus 5/3 And is any integer