► My Limits & Continuity course: https://www.kristakingmath.com/limits-and-continuity-course
The Intermediate Value Theorem is a continuity theorem that allows you to prove that a function has at least one solution or root in a given interval. Oftentimes it's used to show that a graph crosses the x-axis within a specific interval.
You can use the theorem with either a closed or open interval, but a closed interval is more common.
In order to use the Intermediate Value Theorem, the function has to be continuous (and therefore differentiable) on the interval, including at each endpoint. If this condition is met, and you can choose a value along the y-axis that lies between the values of the function at the endpoints of the given interval, then the Intermediate Value Theorem guarantees that there is a point within the interval that will result in the value you picked when you evaluate the function at the point within the interval.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com
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Tagged under: limits continuity, ,continuity,intermediate theorem,calculus,expert,Krista King,educational
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