Mean value theorem | Derivative applications | Differential Calculus | Khan Academy

Intuition behind the Mean Value Theorem
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Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.
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[@HB-qe6ul]

Sometimes I just have Khan's voice playing in the background while I'm doing my homework and IT WORKS. Osmosis method for the win. Khan, your voice is magical.

[@AleTheDLT]

He should do asmr. The mediation videos are cool, but not enough...

[@bsimons09]

"I think this calls for magenta"

[@NStripleseven]

Ben Simons Yep, that makes sense. I may have to start using that.

[@asparwhite86]

I go ahead and skip my text book online website videos(that i pay for) to watch these. You are a great instructor.

[@billybobjoe1335]

Watching this for Calculus class. A note to anyone taking Calculus: it's calculus, don't feel bad if you do poorly at the start.

[@cali1778]

I needed this 👌

[@BlueXDShadow]

Make sure to finish with an A though.

[@morgard211]

@Diogenes TheDog You are greatly underestimating the average student's capabilites. It's actually not that conceptually difficult nor that abstract to undestanding this - it's rather quite simple when you take your time. All these things describe simple real world situations which are easy to wrap your head around. I would say that it's much more admirable if you were capabable of intuitively grasping complex analysis or algebraic topology for example, not just these basic theorems which even average Joe is capable of mastering when given enough time and energy put into it. Telling yourself that it's hard isn't going to help.

[@Peter_1986]

I finished Calculus 3 (Multivariable Calculus) some time ago and I'm watching these videos as a review, and I notice that I have forgotten a lot of things. =P It's nice to see the Mean Value Theorem again, it was a while ago since I last used it. :) You can look forward to Multivariable Calculus by the way, that's a really fun course; it's pretty much a combination of Differential Calculus, Integral Calculus and Linear Algebra in more than two dimensions, and consists a lot of figuring out volumes under surfaces with the help of double integrals etc. I believe there is some Differential Equations stuff involved as well. Either way, it's a really satisfying course.

[@Renee11123]

Thanks Sal, love the colors(big visual learner), you are my hero and you make it so much easier for me to learn calculus.

[@TheZakkattackk]

He's awesome, but I die a bit inside when I read student's comments that say, "ZOMG MY TEACHER SUX, SAL YOU'RE SO COOL!" Sal and people like him have afforded an opportunity that until recently hasn't been available to students, in the regard that a teacher or professor can now articulate application or the big ideas and leave it up to Sal to teach the algebra. I am grateful for this and I plan on assigning Khan lectures as supplemental material while I focus my lecture on application.

[@BellaaRosee]

I have a calculus final exam in a few hours and i've been reading this topic in the textbook for an hour with no luck. this 15 min video explained everything perfectly. Thank you so much, Sal! You are once again saving my sorry butt.

[@dominikb12]

Richard Feynman said that if You cannot explain something easily - You do not understand it. Certainly, Sal understands Mean Value Theorem very well;)

[@Carahloporra]

You make it simple but my professor makes it complicated then gives even more compicated questions on exams...

[@treflipism]

he's explaining the concept not doing your homework

[@Carahloporra]

i never said he was did I smartass?

[@Peter_1986]

treflipism Khan doesn't make his homework either. AmirianoAvenicci is obviously trying to say that his own teacher is too bad at explaining things - and I understand what he means, because I have also had teachers who have confused the hell out of the whole class, and sometimes even managed to confuse themselves.

[@treflipism]

calc one is one of the easiest classes ive ever taken... how do you confuse a whole class with this stuff?

[@Carahloporra]

Yeah well everybody is different and has different professors. So don't think you're some royal shit.

[@guitarlover113]

Dude honestly i say the government should just take all of their money towards improving education in America and just give it to you to make awesome videos. Your the only teacher america needs.

[@catherinewhiting8034]

mean value theorem this calls for...MAGENTA!

[@Dani98664]

This was one of your better videos in terms of being able to understand things. Thank you.

[@zohaaa]

i dont even see the point of going to classes anymore. i just watch these videos and make sense out of my hwrk. salmman ur awesome!

[@marklyles3335]

You took the 'hocus-pocus' out of ( , ) versus [ , ]. Thank You!

[@mariahphilmrazem]

you make my life so much easier you have no idea. my book makes no sense to me but you make it make sense. thank you so much!

[@femiairboy94]

Thank God for people like you on youtube, don’t know what i’ll have done.

[@thatoneguyooty99]

He conveys his message clearly, and makes it easy to understand. brilliant.

[@Alicetalk]

photosynthesis, respiration, mean value theorem...khan academy is always there to help me when i need it (and thank god - my grade would have suffered greatly without it)

[@Pr0x1mo]

Wow dude, such a better explanation than my actual Calc book. Khan's videos, and my Calc for dummies book has made all the convolution and mathematical rhetoric so understandable. It's so much easier to figure out a problem when you understand the "why" of it, and you're not arbitrarily memorizing equations, symbols, and jargon.

[@Kocis19]

Wow man. My second time taking Calculus, never understood this until now, spent hours going through examples and you explained this in 8 minutes. Thanks for your time.

[@kingmeeko]

so good, my calc teacher really doesnt teach and doesnt try to so i really appreciate it. thanks again

[@khanacademy]

You're right that there must be a c other than a or b, but f'(a) or f'(b) might also work (in the case of a line for example). I should have been more clear.

[@surfmimibg]

I love you You are saving us hundreds of dollars each day -fre education. You really should win a Nobel Prize since your more useful than anyone who has won this year!!

[@hellnoid90]

teachers can learn a lot from you... THANK YOU,honestly

[@tw6599]

This is such a great video. Genuinely thank you. You leave no gaps to not understand what's going on

[@dustinnguyen2838]

Rolle's theorem is sometimes referred to exteneded mean value theorem. They are exactly the same, Rolle's theorem just forces you to imply that f(a)=f(b) and then apply the mean value theroem, which then must be 0 because f(a)-f(b)=0

[@karthikesh37]

His way of teaching Captures all of them

[@gobberpooper]

lol before I would read my brother's calc textbook and then come here just so I could grasp the concept easier. That ended by the time I was finished with limits. Now I just come straight here and I've gone through a good chunk of the AP Calculus BC course within 3 days

[@TheDennyvu]

I no totally dont pay attention to my teacher that makes no sense whatsoever, they way you explain this is just that much better

[@michaelvacca2611]

I had to miss class one night and they covered the mean value theorem. I got a little stressed running a few searches on it seeing all of the verbage. In one single video you summed it all up. A Thousand thank you's!

[@kalahauoli355]

i wish you were my teacher haha. seriously , you are so much better. i have my ap calculus exam tomorrow and only found out about this site tonight, i hope others don't repeat my error

[@mwtillotson]

First video I've seen from Khan. Such a great teacher.

[@bolbteppa]

After seeing this in my book for god knows how long and being dumbfounded you clarified everything in 16 mins, clearly. You should write a book in the exact same style as this presentation! I think you'd be the first person to do justice to the label on every single calculus text out there "Ever since i picked up this book, i haven't been afraid of math class - M. Schlezinger - Wisconsin W.A" lol

[@Oboeplayer511]

It's cool if you solve this for a general quadratic; Ax^2+Bx+C for the interval [h,k] (A(h^2)+B(h)+C)-(A(k)^2+B(k)+C))/(h-k)=2Ax+B (derivative of the general quadratic) (A(h^2)-A(k)^2+B(h)-B(k))/(h-k)=2Ax+B (A(h^2-k^2)+B(h-k))/(h-k)=2Ax+B (A(h-k)(h+k)+B(h-k))/(h-k)=2Ax+B A(h+k)+B=2Ax+B A(h+k)=2Ax x=(h+k)/2 so the x-coordinate for any parabola where the average slope is equal to the slope of the derivative at the point is equal to the average of the endpoints of that interval...FASCINATING

[@brHOLLAND]

I really could have used this channel earlier in the semester. Ah well, better late than never. Thanks!

[@RedBishop81]

This was very helpful. I am reviewing for my midterm, and I had a basic grasp on the MVT, but now I feel much more confident in my understanding of the theorem. Thanks. (And many of your other videos are superb as well.)

[@KoltonCyr]

no i've been to my lectures.. it's all theory and he makes it really complicated. And i read the book but this helps a lot more.

[@unrealriot]

my calculus textbook has no examples of it, it just explains concepts and means nothing to solve my problem, but this video really helps, thanks.

[@KoltonCyr]

God, this helped me alot more than my textbook or going to my lecture would have. kudos bro

[@Ltyrann]

Sal, Just want to point something out. According to the mean value theorem f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) You stated many times that c could be any number between a and b and that it could even be a or b (time=07:07) wouldn't that go against the definition? of c being in the interval (a,b) meaning that it must be between a and b? Thanks for the videos, they are of great help!!

[@xwwz4wnn]

u r the best calculus teacher i've ever seen in my life

[@Timureithi]

With khan academy you can always succeed to your fullest potential

[@Sarafara7]

well..if u have a cusp, vertical asymptote, and or cornor, those are discontinuities. so they will not be differentiable at those points (will have no derivatives) but u can have a specific interval that is continuos. i hope that helps :)

[@HeyitsDJCarr]

Can I just say, thank you Sal, you are a freakin' beast. You're videos are entertaining, and they're the only things helping me pass AP Calculus. Thank you!

[@Antilli]

If only teachers could explain it like this. You're right, they always use difficult words to explain everything, while it's not needed. Sometimes I get the feeling they don't understand it themselves and are just repeating what they've been taught and forced into their brains.. Lol.

[@mollierdiag]

Very easy to follow and enjoyable to watch. Thank you.

[@circuithead94]

Oh man thanks a lot for the help and keeping education free and high quality.

[@MrCyborg29]

thank you for explaining open/closed interval

[@solounomas0]

INCREDIBLE!!!

[@zayoob0524]

I watch your lectures after every math lesson I learn...then I get it.

[@jthefoo]

Honestly, you are so awesome, I am going to get an A on my test tomorrow! :)

[@Chrisfathead]

it was just funny the way you phrased it then. there's no doubt khan academy has helped me get through college i wonder what people did before the internet

[@Khattu]

This video helped me to get a 30/30 in my test which helped my CGPA touch 9! thank you !:D

[@LongJohnsMateTom]

Sal you are honestly my hero.

[@RaniOfCoochNahi]

Thank you!! I like your statement that was something like 'it gives you something new to know about the world'. I really need to start approaching all my learning like this--to think "It's nice to understand another little bit of how the world works" instead of my usual, "ugh, maths" attitude. :)

[@legomastermaniac]

You make things so easy. So thankful you post these videos.

[@Koalaslovesloths]

I LOVE the black background! I love not becomong blind while watching it at night xD

[@owimevil]

you're absolutely great! thanks a lot. you helped me in college calculus a lot!

[@mariakurtidis]

thanks so much, i should really just base all my notes off your videos! makes so much more sense now :D

[@OZZl3]

@OZZl3 I saw now that it is: "f is continuous on the closed, finite interval [a, b] and that it is diffrentiable on the open interval (a, b) ...."

[@Joshua6Tube]

U r REALLY GOOD!!! Thanks cause i'm taking Calc 2 class in the fall semester, so i'm trying to study ahead, THANKS ALOT though......and trust me u did great u were not confusing @ all

[@cuzyouneverwalkalone]

"If you gotta know it, you gotta know it...and that tells you something else about the world...so it's interesting that way." Gotta love observations about life during math class :D

[@emadrio]

Seriously, if you wrote a math book, I would easily pay 25% more for your book then the traditional math books I have to read. Thanks a bunch for posting

[@TheHumanMC]

VAVERAGE!! on a serious note, this video helped a lot. i hope i dont fail my math exam tmrw.

[@beastlt12]

Very clear video. Thanks for the good presentation.

[@1demp]

thats right in Khan we trust"preach!

[@georgya3xx]

Than you so much!

[@A-Noodles]

Thank you because I really didn't get mvt until this video

[@calegoethals4575]

This guy really knows his colors

[@Quarker]

Clear explanation. Great explanation!

[@Darkryers]

Grreat stuff! Thanks, very straightforward.

[@krittika21]

thanks a lot sal....i rather make use of my time watching ur videos...than listen to my professors ...don't understand a word of what they say...!:D

[@dustinnguyen2838]

What is the interval of your equation? Just find the slope from the endpoints of your interval, and then make your derivative equal to the same slope

[@TopBaller00]

Skip to 12:20

[@alii9346]

Literally saved 13mins of my life. ty!

[@kabeer069]

thanks dude u made it look so easy i get it 100percent

[@arizona_iced_out_boy]

What is this professor's name? I know this was almost 6 years ago but I just want this guy to know that he explained incredibly clear what MVT is.

[@weathercircle]

that makes so much more sense. omg. thank you.

[@michalchik]

Yes, i know, but he set two requirements, continuous and differentiable. Differentiable requires continuous so his first requirement is redundant.

[@patross789]

This video was very helpful, thank you very much.

[@silkydude]

Great stuff man... You have a gift.... thank you for sharing it with the world...

[@KeiserWilliam]

This is an amazing video! Thank you for making this abstruse concept so understandable. 10/10!

[@NetITGeeks]

THANK YOU SOOOOOOO MUCH.

[@nayanakr]

Like the way you explained it. Thank you.

[@deathmoonkiller]

I feels good after watching this, my lecturer definitely confused me everything about this.

[@superomega16]

And here I thought you were just a 11yr old boy from america. Good for you.

[@Alex-bc3tt]

Once again you nailed it Sal... I now have a Reason to sleep with a smile on my face. Keep up the great work

[@cnx33]

can you please talk about the extreme value and intermediate value theorem?? :)

[@zero3609]

Sal.... You are AWESOME, thank you

[@Nuhjeea]

wow, this video is very useful. Thanks!

[@xROFLawsonx]

Amazing! I didn't even realize this. Thanks.

[@hmmmmm12]

You're great at explaining things, thanks a lot!

[@OZZl3]

I just noticed today according to "Calculus A Complete Course - Robert A. Adams (Sixth Editon)" page 129 that they say on a OPEN intervall not on a closed intervall, but maybe that doesn't matter?

[@joshbeach9147]

thank you so much! I zoned out in class today this definitely helped me!

[@Waranle]

Thank you alot Sam

[@KurkpropBattery]

Can you make a video to teach teachers and lecturers how to teach!!

[@sreerajvishwanathan9150]

Thanks for the best explanation

[@utkar1]

you are AWESOME.. but why are we studying this theorem.. if you could give some applications of it, that would make the existence of this theorem more sense. Thanks :)

[@TheUberTurtle1]

Thank you based Khan academy

[@ztpo]

easy to understand thanksssss