I asked a question earlier about open and closed intervals, so why did my teacher say this was wrong?

Determine any values of c in the interval [0,2pi] for which f'(x) = 0.

f(x) = cos x

My answer was:

f'(x) = -sin x

set equal to 0

-sin x = 0

x = 0, pi, 2pi

she said

0/7 points: 0 and 2pi are not acceptable answers

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She asked if the function can have Rolle's Theorem applied and if it can, find any values of c where f'(c) = 0

You confirmed my suspicion that this problem is related to mean value theorem or a special case of it in Rolle's theorem. Both theorems stipulate that there is a point c on the open (emphasis on open) interval where slope equals the average rate of change on the closed interval [a,b]

That makes sense. So in other words it doesn't matter that it is closed, when you use Rolle's Theorem your always looking on the open interval. Thanks so much Imtiazur!

If the problem says to find a point c as stipulated in Rolle's theorem, then you must specify only those points that are on the open interval. Your teacher will take points from you if you show x values in the closed (but not on the open interval) or outside the interval.

Hope this helps.

Not sure how you concluded that the boundary points will have infinite slopes.

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