Intermediate value theorem example | Existence theorems | AP Calculus AB | Khan Academy

[@shadabali2302]

Please, Give the counter example regarding every thoerm. It's more useful for better understanding. Thanks!

[@Zendembe]

It looks so easy on screen...but once it's on paper that's another case...

[@ridasiddique8949]

GREAT PLATFORM FOR LEARNING

[@kushagramudgal398]

Helped a lot.

[@jun341]

why does the answer "f(c) equals to zero for x between -2 and 1" false? because there's no domain restriction for the f(x), can't the graph just cross f(x) equals 0 first before going up to f(x) equals 6

[@chiragkaudan9787]

Because it is not guaranteed. The question asks which of the following is guaranteed, meaning absolutely true no matter what. The function f(x) could in fact equal 0 for x between -2 and 1 however that is NOT guaranteed. The graph could cross f(x) equals 0 but it also could not. We don't know and we have no information on that and no way to tell whether it crosses 0 or not. All we know for sure is that it has to take on every value between 3 and 6 at least once. Again we're not saying that f(x) cannot equal 0, we are saying that it is not guaranteed. Meanwhile, the correct answer f(c)=4 for at least one c between -2 and 1 is a guaranteed statement 100% of the time for this situation. There is no doubt. Hopefully I made this clear.

[@rizdhium]

That's exactly what Mr.Purcell said on the book

[@ashishcmslpc]

It should be kn open interval

[@Handle12456]

I got a question with open interval ]1,2[, how do I deal wt that? I m so confused

[@starbunny3354]

I think we cant state ivt with open intervals