► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course
Rolle's theorem can be used to show that a function has a horizontal tangent line inside an interval. If you can show that a function is continuous over an interval, differentiable over the same interval, and that the function has the same value at the endpoints of the interval, then you can use Rolle's theorem. Without each of these three conditions being met, Rolle's theorem cannot be applied.
If however you can show that these three conditions are all met, then Rolle's theorem proves that there is a horizontal tangent line somewhere in the interval.
Remember, a function has a horizontal tangent line wherever it changes direction from increasing to decreasing or vice versa. Therefore, if you can prove the existence of a horizontal tangent line, you've also proven the existence of a local extrema, which means you've got a local maximum or a local minimum.
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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: calculus,expert,Krista King,local extrema,local maximum,horizontal tangent line,local min,educational, ,local minimum,local max,derivatives,rolle' theorem,calculus expert
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