I want to give an informal proof of the intermediate value theorem to my calculus students. They have just learned about continuity and they don't know yet about derivatives among more other advanced topics. Do you think it's possible?

Cheyanne Jefferson

Cheyanne Jefferson

Open question

2022-08-13

I want to give an informal proof of the intermediate value theorem to my calculus students. They have just learned about continuity and they don't know yet about derivatives among more other advanced topics.
Do you think it's possible?

Answer & Explanation

Jazmin Cameron

Jazmin Cameron

Beginner2022-08-14Added 16 answers

Assume that f ( a ) < c < f ( b ), bisect the interval [ a , b ] into [ a 2 , b 2 ] such that f ( a 2 ) < c < f ( b 2 ) (if this fails, that means we have reached the goal). Proceed this again to get [ a 3 , b 3 ]... so the left endpoints and right endpoints converge to a point η, continuity then implies f ( η ) = c.
sapetih1i

sapetih1i

Beginner2022-08-15Added 1 answers

Nice, thanks

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