Quick question about extrema on an open interval

Okay, so I'm given f(x) = cos(x) / (1 + sin^2(x)). The question says "find the intervals for which f is increasing or decreasing and locate all relative extrema on (0, 2pi)."

Now, I've already solved this; I just have one question.

There are relative extrema at the points x = 0, x = pi, and x = 2pi. The question gives me an open interval, so I don't know if I'm supposed to include the relative extrema at x = 0 and x = 2pi. This class loves giving trick questions.

Any help is appreciated!

Question

Quick question about extrema on an open interval

Okay, so I'm given f(x) = cos(x) / (1 + sin^2(x)). The question says "find the intervals for which f is increasing or decreasing and locate all relative extrema on (0, 2pi)."

Now, I've already solved this; I just have one question.

There are relative extrema at the points x = 0, x = pi, and x = 2pi. The question gives me an open interval, so I don't know if I'm supposed to include the relative extrema at x = 0 and x = 2pi. This class loves giving trick questions. 

Any help is appreciated!

solomonzelman · Answer

open interval is not included in a function. Don't include it.

solomonzelman · Answer

it wouldn't make sense to say that local max (for instance) is (a,b) if this point (a,b) is not even on a function... right?

anonymous · Answer

That's what I was thinking, I just needed some confirmation. Thank you, Solomon!

solomonzelman · Answer

Anytime:)

solomonzelman · Answer

be always careful not to exceed the interval given:)