Mean value theorem application | Existence theorems | AP Calculus AB | Khan Academy

Even if a cop never spots you while you are speeding, he can still infer when you must have been speeding... Created by Sal Khan.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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[armangrigoryan]

It's so good to see Calculus theorems' application in real life, for it makes you believe you aren't learning something useless.

[benjaminlehmann]

They have this traffic enforcement system in the UK. It's called Average Speed Checking.

[chiramana_]

Excellent ✨
Thank you so much, sir. Keep growing 🌱

[sid]

I would love to watch someone explain this in court, heck I'll overspeed and then challenge them in court! That'll be

[ajaykumargangavarapu]

May I know from where your creating this much content...

[unaliveeveryonenow]

Just divide the time interval in half. At least in one of the halves average speed must have been over or equal to 80. Divide until the time interval is small enough to conclude that average speed is practically interchangeable with momentary speed.

[erickmaurer]

This is good a good legal argument, assuming one know's truly understands and comprehends the mean value theorem. It has been used to argue the validity of their radar readings, in pertinence to how many miles per hour one was actually traveling and have successfully won the case by simply having a background in mathematics. Fringe benefits.

[rohithkarkala]

Great video as always keep up the good work

[MindofScience]

There is a reason these passes exempt you from MVT speeding... no one would use them otherwise.

[alektad]

They should increase speed limit by 10 mph and enforce this law,

[jani]

I don't know your name but your example is awesome and I understood it's awesome way of teaching

[sindhumarudhu]

In engineering field how mean value theorem is applicable with example

[dopesheepify]

You could just say it's how averages work without having to explain the MVT to the layman. 1 hour to go 80 miles? That's an average of 80 mph! 80 is above 55 so there's no way you didn't speed.

The MVT makes it mathematically precise I guess. Are prosecutors required to provide a rigorous proof in any country? It'd be awesome if they were.

[wazawoo]

This is how multiple European countries (Italy for sure) give citations on certain roads. Your license plate is recorded at a certain checkpoint, and if you reach the next one under the specified time, you are sent a ticket. 

[Ostrya]

The Florida Turnpike issues speeding tickets in this manner.

[mr.gakhar]

Its really cool. CBSE exempted us from studying the Rolle's and mean value theorem. But, i 'm lucky that i didn't opt to leave it😃

[Trnado]

the only way you will get out of that speeding ticket is to turn into a really, really small person to get some quantum mechanics goin ...

[daedra]

Yeah, my only to out-reason the cops was teleportation. Guess I'm out of luck Sal :(

[soundaryareddy]

What if the person speeds up and then stops the car for a moment and then again travels with a speed to get a speed less than the speed limit?Can we still apply the theorem?

[changyue]

I will not get a ticket if I drive 80m/h for 59min, and wait couple hours then drive to next toll booth. According to MVT, I will not get a ticket even I speed over 80 for most part.