The Mean Value Theorem

[lavya41]

patrick, can we see your face? I am interested:)

[patrickJMT]

@lavya41 i am not sure who everyone thinks that is on my channel page.... :)

[1mat3u5z1]

i wanna take a minute and thank you for postin all these videos, thanx to you, i am doing amazing in my calc class and i feel less stressed knowin that you also have videos for calc 2, 3, nd differential questions. Thanx Patrick you r my math hero

[funmore556]

I LOVE YOU SO MUCH RIGHT NOW! Saving me tons of money!

[knockknockchurch]

why are most of the suggested videos about atheism?

[juveforez]

dude why are my teachers so useless ?

[iluvishreddish]

can you make a video about the mean value theorem for integrals? :-D please and thank you

[TheAndrewHartness]

Very helpful. Thank you!

[Yamikaiba123]

Hi; I'm doing a quiz correction, and I'm confident I need to use the Mean Value theorem on this question that it had not dawned on me to do so at the time.

It gives me the function f(x), then asks me to find the average value of f on [2,5]. In the example you gave, is f(c) the average value of f?

[Yamikaiba123]

@Yamikaiba123 I mean fprime(c)

[Yamikaiba123]

@Yamikaiba123 Now that I'm trying it; I think f(c) is the average value of f, but that I have to first find f prime (c) using MVT, then use c in f(c).

[Raymond10011]

Whenever im searching for math videos and i see you name pop up, i get all excited :D

[apalm111]

So helpful! I like the hard examples!

[khgkjjhgfhjdhgsgfhf]

You just saved me in calculus. Thank you. I am now one step closer to completing calculus with a good grad my junior year in high school. You are awesome. <3

[jakkabify]

Wtf is this? :o I was watching Lia Shevinchi or something like that and it brought me here?!

[Nazilyagasanova1993]

you video was extremely helpful, but please next time if the examples had simpler function it would be easier to understand(:

[patrickJMT]

@Nazilyagasanova1993 some people yell at me for easier examples, some yell for harder :)

[mattadorespie]

I am a junior in high school in Calc A, your videos are especially helpful. My math teacher literally assigns homework and never teaches us how to do it. I'm so glad I found your videos, especially since I will take Calc BC next year as a senior. Thanks a lot dude, you're very helpful. :)

[luxebaby41]

marry me, you math god.

[patrickJMT]

@luxebaby41 ha, i have had lots of ' i love you ' and ' marry me ' comments here recently :)

[historyfairgirl]

ap calc midterm tomorrow. last midterm i will ever take in highschool. finish strong, finish strong.

[CrazyFile]

Thanks so much.. You're an amazing teacher!

[YummyCookiesHuh]

Dear patrickJMT,

If I had a dollar for every time you helped me with math, I would be richer than Bill Gates

From,

A fellow math guy

[TheFungalSpore]

on finals night you are a God!

[cLoCKyy8]

Thank you! :) my lecturer is stupid..

[carlopez3]

Thanks for the help!!!

[TheGoldBoltz]

god you're such a beast

[MONSQUEEKY]

dude you saved my life



[franknguyen007]

Great vid, thanks a lot.

[jegerjon1991]

Great video. Thank you! It is impressive how you can explain this so much better than my calculus teacher. It is actually extremely simple!

[slymn641]

really thank you so much ur videos help to me so much tomorrow i have final exam before i got nothing until now thank you :)



[ExtremeVoltages]

very nice work keep it up sir

[Calico7358]

Good stuff!

[Sk8MakeVideo]

youre way better than my teacher and she's IB certified lol

[smarttarts]

You should really write a math book. It'd make so much more sense than the ones my school buys

[robrobbyrobrob]

my favourite of your vids

[ZMclovinFan64]

Great job. Thank you for giving such a simple explanation.I will definitely recommend this to my friends. This is going to help me so much for my calc finally. Why can't you be my teacher instead of my weird old professor

[MRDUE18]

I second that thought! Wish I saw this earlier on.

[linneaeboralis]

These videos are awesome! I wish I discovered them sooner instead of at the end of my term! I bet because of your videos I'll do way better on my final :) Thank you so much for taking the time to post these!

[drillfang25]

Thanks for all your great videos! I go to class and come home extremely frustrated cause my teacher sucks. Once I watch your videos I feel a lot better. I actually kind of like calculus cause of you. thanks for the videos and keep em coming :)

[rabi1412]

it was helpful ..thanks ^_^

[MrNickyWilly]

calc final tomorrow. your videos might help me actually pass!

[blazekayn]

Now I don't have to fail my calc final!

[12345beesquared]

you are a life saver. thanks so much



[scuarliens]

Calc final in 3 hours! You sir, have just saved my life!

[MrUnicornlover121]

I have a calc final tomorrow, and this just saved me. You're the man!

[MyMaggers]

do they really have to put an advertisement right in the middle of the video...thanks youtube

[patrickJMT]

@MyMaggers thanks for letting me know, i got it removed.

[xAndrewPaquettex]

Thanks. Helps me to fill in the gaps in my math knowledge, you're very helpful.

[SaudiCanadianBoy]

how come google or youtube hasnt awarded you yet ?? so shame on them!

[jhembro13]

I have a final exam this week. I have been taking calculus through distance learning and have no teacher which was frustrating. But thanks to your video, I can finally grasp the concept of calculus and feeling confident for the final exam! Thank you!

[vivalaliberty]

you Sir rock, you just made me understand The Mean-Value Theorem with this video. Thanks :o)

[djkPVUSD]

Your videos are great, but I'm too ADD for this, do you know where I can find a condensed version?

[Einsteined]

Thanks, this will help me on my test

[saraaarofl]

Thank you so much :D

[JustPassingByGuy]

i can honestly say without a hint of exaggeration that i learn more in these 10 - 15 min vids you make, than i do during a one hour and forty min lecture by my teacher.  i just wish you did calc based physics too.

[ThugOrNotTV]

Thanks Patrick, I'm maybe a thug wink wink but I appreciate the calc help bro!

[irivera1894]

THANK YOU! :)

[caralwolf]

totally acing my quiz on this tomorrow!!!! thank you so so so much

[mage1413]

yo man, I am in life science first year, and i HAVE to take calc for my program even though i dont need it in the future...and i hate calc. however watching this videos makes everything so much easier, its practically motivating me to do good in school. keep up the good work

[jumpeygirl101]

If there are two different points on the graph where slope f'(c)=f'(x) slope how would you find the second point?Like the example you just did found one point, is there a way to get another point? I hope my question makes sense lol

Thanks!

[LordBunbuns]

Anyone else cramming for a test/final?

[silverflame92]

@LordBunbuns yea dude..

[dou]

THANK YOU SO MUCH!!!!!!!!!!!!!!!!!!!!!!

[ebk23]

thank you! i'm from sweden, but our calculus book is in english for some reason. your videos help a lot, both when it comes to understanding the subject and to learning the english terminology. tack så mycket!

[Maydaysdifference]

calc 2 exam.......................thx

[iiottoii]

sooooooooooooo helpful calc quiz tomorrow

[SamihCAA]

MAN! This helped refresh things up about M.V.T. (: Thank you thank you!

[DARR0Y]

Thanks (again) Pat! Was ripping my hair out over this unit cause I didn't feel like my teacher did a very good job explaining it

[PerfectPitchPianoMan]

ur awesome patrickJMT!!!

[23SuS23]

just wondering, do you have a degree in mathematics or something similar?

[adaniel140]

Thanks!

[kenneth12345678910]

If what I said previously was correct wouldn't that simply make the answer be 1 + square root of 7 over 9 cubed

[kenneth12345678910]

11:48 When you rephrased the cuberoot as a power of a fraction ... did you forget to rewrite the 3. Because it seemed to vanish, or I am not sure if thats how you do it, but it looks more like you forgot to put the 3 in there after that

[Caledrith]

There are 16 Justin Bieber fans who watched this video

[TheSuperBirdLady]

I'm kinda confused about the [a,b] and (a,b) difference and when you are given an equation, where do you find [a,b] if you were to graph it?

[supersinghification2]

thanks a lot for such a good explaination! you are the best!

[goditja]

Thank you so much for your videos...I learn more here watching your videos, than in school..

[tutuuo]

stop commenting to get the top comment, and listen to him.

[bobschneeify]

Your videos are very helpful. Thanks for taking the time to post them..:-]

[patrickJMT]

@bobschneeify my pleasure! i post em cause of all the nice comments i get, like from you.

[ADMlN02]

You said root functions are continuous on their domain which you said D(-infinity,infinity), isn't the domain suppose to be x>=0 because you cannot have a negative number inside a root?

[patrickJMT]

@ADMlN02 you can have a negative inside an odd powered root, which this is.

[Parkyy16]

@patrickJMT Totally forgot about that. Thanks. I came from your website to youtube to look through the comments.

[cjUSA867]

thanks dude that was REALLY helpful

[katerinawsy]

Patrick, thank you. I used to be so good at math. I loved to read, so in high school all I'd do is read during math class. I maintained a minimum of an A-. Then here comes college where I can skip class altogether. Note: I have been going to class most of the time, but I'm very flexible about skipping. Obviously, I regretted it when I got a poor grade on our 1st midterm. Which was way too hard, even the professor said so. But for this midterm, I'm feeling so much more confidant, thanks to you!

[patrickJMT]

@katerinawsy glad i could help and : go to class. i missed about 5 classes my whole college experience.

[patrickJMT]

@katerinawsy AND i was talking a full course load and working 40 hours a week

[6BURG9]

1:18 squiggle face



[katerinawsy]

@6BURG9 lol. I see that.

[imyourfather101]

woot! lefty like me :D

[patelvp100]

dude you worked a problem thats too hard for a tutorial, step it down a notch

[patrickJMT]

@patelvp100 lol, i dont know if you are joking or not

[SuperYooshii]

Finally! A math teacher I can understand! (both in terms of vocabulary and diction) :p

[rharbour22]

Thank you so much for teaching me what my AP Calculus AB teacher can't.

You are such a great person!

[Yhwhian]

You're going to be famous!

A good teacher holds influence over the students!

[patrickJMT]

@Yhwhian well, i do not want to have influence over anyone, unless it is to encourage them to study and to work hard : )

[tobefree21pop]

thx u so much. I LOVe ur WORK!!

[William31389]

I think the problem was a little over kill but over all I have gotten something out of it. So, thanks for posting. Great Job!!!

[MirandaScaresYou]

You are amazing, thank you!

[xbebejosiex]

thanks man!! got test monday! you are alot of help!

[kkeelllyyy]

thank you, seriously thank you lol

[RarRarJake]

that is a great example i feel behind early on my class, i am trying to catch up with the exam coming up thursday been studying all weekend, hopefully this helps. I really do not want to take a W in the class. I want an A.

[IntensityInTenCitiez]

you are my lifesaver

[jpmoench21]

i wish i had you as a teacher!

[sanqie]

Cheers dude! Your videos are so great :D

[Richardhuang70]

godly explanations. thank you very much =)

[ndimhotsi]

thanks man this is really helping me in my calculus class

[ayanmosh]

Thanks man

[DDns]

god damn advertisements somehow shut the video off.. I HATE YOutube now.......damiittt

[DDns]

@DDns But thank you very much for the videos they are amazing and helping me soo mcuh in my calc class

[Joshua6Tube]

Thanks a lot! u did excellent!, but i just got lost @ the very end, i get it now, but can u please explain what happened to the x-1?

[milkeatscereal]

great but i think you couldve done some easier problem

[jormoria]

you are mucho chingon, i like it

[TheNumber2Pencil546]

please answer: what is the difference between the rolles theorem and mean value theorem? are they essentially the same?

[luckyfanarun]

thanks a lot, i understood what i had found so like crazy in the class.

[lpperalta1]

if a click on ads while watching your video, will you get paid?

[tupacsomething69]

i understand everything from my lectures and can do most of the tutorial problems, but i still dont get a pass, what am i doing wrong

[AlyAmmad]

This video was really helpful. Thanks to you I was able to solve the questions in the book. =)

[frankiechan10]

it was so great!

thanks patrick!!

from a Hong Kong student :)

[dandt777]

thanks a lot! I was reviewing this concept for the CLEP exam. One question, isn't f(x) imaginary when x<1? because a negative under a radical yields and i right? thanks once again!

[MasterThief1324]

12:55: what property is that whereby you can raise both sides of an equation to a power and still maintain the equality statement?

[daug27]

@MasterThief1324 well: a=b => a*a=b*b or whatever power you raise both sides.

[MasterThief1324]

Read the wikipedia article on the mean value theorem. There's a photograph on the side with the caption "The Government of Beijing celebrates the Mean Value Theorem"

[Th1x4nG]

People like you are what makes YouTube this great. I'm really struggling with my math class this year but I'm sure I'll manage thanks to your vids!

[Ericplaysdrums]

Patrick, you're the best.

[valdivia562]

man yours videos really help especially when my AP exam is an hour and 30 minutes away

[Ensivion]

thanks :D good luck on the AP exams everyone.

[ilovezb1]

This helped so much for last minute studying for the AP calc. exam tomorrow. Thanks!

[SparkleyEyes08]

you should really consider teaching a calculus course...bc TRUST ME today's calc teachers are quite lacking...

[tickled41]

thank you soooo much T__T

[jnrenoch]

great

[lilsteph553]

thanks you this was great!!!

[peachsarangblue]

thanks for the video, but just one thing: 1:05 you said "here's some x-coordinate a and here's some y-coordinate b" but you labeled b on the x-axis. was that intentional or am i missing something? but other than thank ty for a gr8 14 minute episode of maths, really appreciate it because i can pause and replay this anytime and you did a really good job explaning

[Gijzzje]

thanks a lot, explained very clearly, and saved me for about 3 hours of learning =)

[BeatTheChallenger]

I LOVE YOU

[Shryne]

I dunno why, but learning math at home is easier than sitting in class...

[MultiMoe91]

i'm confused :(

[skatty14]

Thanks for the great math videos, I can't help but drooling over your immaculate white board, it is an absolute beauty! (especially when calculus problems are neatly strewn across it)

[patrickJMT]

@skatty14 lol



[skatty14]

@patrickJMT Oh, and I actually did my math problems involving the mean values theorem in like 5mins instead of spending an hour staring at them in resentment. You are the 2nd math god I will pronounce today (the first be the "Pi is (still) wrong" girl, her video is genius, you should check it out! :) Merci again!

[Yeri0413]

if the original function is x^3+2x+1 [-2,1] and with MVT, is the answer both 1 and -1?or is it just -1??

[okok622]

how this

[-∞,∞]

mean continuous at everywhere

i really dont get it

[skatty14]

@okok622 the domain of the function can have any value for x over that interval (e.g. it can have any real number as an x value), thus it will not have any "holes" (undefined- like when denominator is zero) in the graph at any point and is continuous. Hope that helps? :)

[Mindfor2012]

YOU SAVED MY LIFE!!!!

[jskuzma]

Great Videos.

I appreciate how you take the time to do these.

Thanks!

[0zero0zero]

Great video, thank you so much!!!!

[agiangnguyen]

can this MVT valid in space? what i meant is in multi-dimensional space.

[ErKLL1970]

wow.. u explained it so much better than my teacher..

[pigeonman07740]

Thank you so much. This video alone taught me more than my teacher taught in the last chapter and a half. You may have saved my graduation. Thank you again

[vickmck]

Still, liked the vid. :-)

[vickmck]

Hey. Has nobody noticed this guy's error? 1-3+1 (Example 1) does not equal -3! It equals -1.

[LaQuishaT]

Question: if the a isn't exactly given, all you have is a graph and the be is 12. Then what do I do? If you have the single variable calculus book, it's in there...thanks

[TheAlbania91]

I appreciate what you're doing, this is noble!

I prefer watching a single video for a whole chapter, for like 10 min, and understand everything, rather than my copybook (a mess I have to say).

[peanutbutterlips]

Thank you so much! :)

[ienjoymusic27]

i love you...

i have my calc final tomorrow...GAAHHHHH

[Dayzheart]

:D' AN UHAAAAAH  moment thank you today i have the final and i was stuck in this :D thank you wish you all the best

[Dayzheart]

:D' AN UHAAAAAH moment thank you today i have the final and i was stuck in this :D  thank you wish you all the best

[Jaesun215]

Thank you Mr. Patrick. This helped a lot :)

[EcFXSN1P3RX]

11 people who disliked this video need to derive their car off a cliff :D

[hammam123]

you are a great man. i don't know how to thank you.

[karenbeaton1]

Breathtakingly simplified

[sanjaykrish8719]

Should have chosen a simple function as the objective is to explain mean value theorem..

[iamtallerthanher]

Great video. Tied a few loose ends for me. Like many of those writing comments here, I can testify the lecturer I had for Advanced Calculus didn't go through the MVT like so.

[Rhonnie2094]

Haha, wassup all of y'all studying for finals! Haha

[jassijatt44]

That was a great help thanx a lot sir.....