Mean Value Theorem with Example

Learn the Mean Value Theorem in this video and see an example problem. Video tutorial by Mario's Math Tutoring.
0:18 What is the Mean Value Theorem (MVT)
0:46 What is Continuous
0:55 What is Differentiable
2:39 Example 1 f(x)=x^3 + 4x [-1,1]
4:20 Calculating the Slope (Avg. Rate of Change)
4:43 Taking the Derivative
5:15 Graphing the Polynomial
Related Videos:
Rolle's Theorem with Examples
• Rolle's Theorem with E...
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[@MariosMathTutoring]

If you liked this video definitely see this video I did on Rolle's Theorem here: kzbin.info/www/bejne/g2PFY6KhYs-npZY

[@fallindavoid]

I wish I had a professor like you in my class !

[@MariosMathTutoring]

Awww thanks!

[@tbg6070]

I don't know why but there something about the way you phrased it that just made it click; thank you!

[@MariosMathTutoring]

You’re welcome Ode! Glad the way I explained it helped you!

[@zechen4009]

That is one beautiful skull, sir

[@marcmouawad8002]

I still havent learned this theorem at school (supposed to learn it on tuesday) and now i perfectly know it because of you thank you you’re one of the greatest math teacher i have seen

[@MariosMathTutoring]

Glad you like my videos Marc! And that’s great that you are being so proactive about your class and learning math!

[@DanT-iu6oc]

best explanation of MVT on the whole darn internet. You, sir, are a legend!

[@MariosMathTutoring]

Glad you liked my video Dan!

[@Trang-po1zj]

watching this the day before my test and i understood everything right away! thank you so much!

[@aaliyahvarona5409]

This may be an old video, but it is still very helpful! My teacher provided us with an unclear explanation, 2 examples, and then expected us to understand. But, this video made this topic much more clear. Thank you, sir!

[@blesskale4267]

Awesome. There is this Amazing feeling watching your tutorial.Your video resolution even makes the lesson more in person. Well explained sir.Thanks

[@MariosMathTutoring]

+Bless Kale your welcome.

[@jonathansimon2226]

Best explanation I've ever came across. Thank you!

[@shiiaizah2858]

Literally I couldn't understand this not from my teacher or friends or book but your video made me understand everything. Thank you so much!

[@phlo-m7237]

what a great explanation, very smooth. Thank you.

[@amazinggrac7]

king you literally saved me i had no idea what mean value theorem was and i watched this video snd your intermediate value theorem vid the night before my test and i got an A+! you’re the best👍🏼👍🏼

[@hamdimohammed2541]

I like it when teachers speed up the basic algebra parts on videos! If someone is watching this calculus lesson, he must have did tons of algebra before, so it is just a waste of time to explain every little detail. Thanks sir, quick and neat tutorial!

[@annaschafhauser3400]

thank you for saving my midterm grade your videos are saving me right now

[@kariuki5308]

Best explanation so far. Thank you so much

[@amycontreras5897]

You made everything so simple thank u so much !!!

[@faalu]

Great video, thanks!

[@veronicasantamaria278]

This is by far the best explanation of MVT I have heard.. Thank you so much!!

[@amalraj2825]

right broooo

[@DAU-sx1rl]

Thanks for the clear and thorough explanation

[@fluffowuffo122]

Thank you for this video! I'm studying for my final rn, and this is something I wasn't taught(unless I just forget) that the exam might cover. Thank you! ^w^

[@drewmastronardi7333]

Simply Fantastic.

[@shamelsinha1626]

amazing explained it so simply! Thanks man!

[@JohnnyMac-js3se]

Great video, might do well tomorrow thanks to you.

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Very good. Thanks 🙏

[@caleb_himself6007]

Thank you for this video really is gonna help me out

[@knightsoftheroundpeople2676]

Thank you so much!

[@Nature-cl4kb]

thank you

[@andreis8100]

thank you!

[@TheXixi743]

Mario, you are a star! Thank you!!

[@MariosMathTutoring]

Glad my video helped you!

[@billygraham5589]

Is the average rate of changing between any two points on a plot of a continuous function always equal to the slope of a straight line between the two points? (Sort of like a state function for enthalpy or entropy in chemistry.)

[@hwitdajuice]

thank you this helped me with my home work so much

[@ranjinisengupta1661]

Love your videos You seem to make maths so much more interesting 👍😊

[@MariosMathTutoring]

+Ranjini Sengupta Thanks for being part of the channel I’m glad my math videos are helping you!

[@tcolondovich2996]

Thank you for posting this video. It's really nice to hear the audio on the speaker channels instead of the subwoofer channel. I almost want to switch back to a stereo system with the subwoofer channel blended in, but then I remember how much better this sounds. I'm not sure where several different math tutors including Khan academy found video editing software that puts all the sound onto the subwoofer channel. I guess that's what I get for watching free videos, and probably what they got for free software.

[@MariosMathTutoring]

You’re welcome! Glad you liked the video!

[@Mike-ks6qu]

Mario...you sir are a great teacher!! Thank you!!

[@MariosMathTutoring]

Glad you like my teaching style Mike!

[@bahahabahaha4146]

very nice video thanks for the help dude. swag on

[@samherschler538]

Incredibly helpful. Many thanks.

[@MariosMathTutoring]

You’re welcome Sam! Glad my video helped you!

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Love this channel! So helpful.

[@MariosMathTutoring]

Glad you like the channel!

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where to use it. is it useable in stock market or any were else?

[@user-vu2vf4yc7v]

Thank you. That was beneficial

[@MariosMathTutoring]

+Fatma Albalushi your welcome! Glad my video was helpful.

[@skippycochrane1839]

These videos are helping a lot keep it up!

[@MariosMathTutoring]

Great! Glad my videos are helping you!

[@prasannakumarpalvai9478]

Thank you bro I want cauchy's mean value theorem

[@arsh_patel024]

Thanks alot sir for explaining this... Love from India❤️❤️❤️

[@MariosMathTutoring]

You’re welcome Adarsh! Glad you liked the video!

[@blake5020]

So helpful man! I have a math test tomorrow, and I’m gonna come back and comment what I got.

[@muhamad.Barzani]

perfect tutorial in every way

[@MariosMathTutoring]

Thank you!

[@helloooitsmeami___]

Sir thankyou so much.. Every thing is clear now ☺

[@MariosMathTutoring]

Great 👍

[@danieldeayalaboaventuratho3319]

Great Explanation!

[@MariosMathTutoring]

Glad you liked my explanation of the the Mean Value Theorem Daniel!

[@eirtiuwrkhgfasd]

Thank you ❤

[@MariosMathTutoring]

You're welcome 😊

[@parsat5567]

Thanks it really helped

[@MariosMathTutoring]

You’re welcome Parsa!

[@Proudmuslimah123]

Great video!!! thank you so much! I am cramming for an exam next week!

[@MariosMathTutoring]

You’re welcome! And good luck!

[@Proudmuslimah123]

@@MariosMathTutoring Thank you!!

[@ev221b4]

perfect!

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I love you bro you made my math life easy

[@MariosMathTutoring]

Glad my math videos are helping you Leenard!

[@sweatstallion8437]

I feel like he really loooking at me like he just knows. Thank you!

[@arnavnayak576]

thank you so much sir

[@MariosMathTutoring]

Most welcome

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I thik u understand maths clearly bcuz u explain it simply..hats off u sir..

[@MariosMathTutoring]

Glad you appreciate my videos Sajjad!

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Thanks you rock!

[@MariosMathTutoring]

Your welcome! Glad you liked my video!

[@Dumbo9]

Thanks alot !

[@MariosMathTutoring]

You’re welcome!

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you are amazing

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Oh my God, I think you just saved my calc grade! Thank you so much!

[@MariosMathTutoring]

You’re welcome Kaitlin! Glad my video helped you!

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helping me get thru math 😓 thanks professor

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if I had you as my prof I would be doing a whole lot better, thanks!!

[@funnyvideo-cg6lo]

nice.thanks

[@MariosMathTutoring]

You’re welcome!

[@amra.haleem5175]

I like to ask you after seeing this tutorial; what are the applications of knowing this theorem?

[@josep_romero]

Thanks so much, saved my butt!

[@MariosMathTutoring]

You’re welcome Josep!

[@ashimamohanty8674]

Awesome explanation...love from India

[@MariosMathTutoring]

Thanks Ashima!

[@humanbeing4109]

AWESOME.

[@MariosMathTutoring]

Glad you liked my video!

[@siddharthsingh5829]

Thanks Sir

[@MariosMathTutoring]

You’re welcome Siddharth!

[@calvintompane]

Keep up with the good work. I'm repeating my Advanced Calculus...It'd really mean a lot if you post more videos of it.

[@MariosMathTutoring]

Thanks for your positive feedback. I’m glad my video helped you.

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Is this video helpful for graduation 2nd year?

[@husna8132]

That was gud sir thank you vry mch😊😊

[@MariosMathTutoring]

You’re welcome Haroon!

[@Fadic4]

You're the best

[@MariosMathTutoring]

Thanks!

[@Accountmatics]

Did you have Extreme Value Theorem video?

[@MariosMathTutoring]

To find the relative extrema...the turning points on a graph you will need to find the derivative and set that equal to zero...I talk about that in this video here Finding Turning Points Using Difference Quotient kzbin.info/www/bejne/g3zZcoaFdqx9jKM

[@nabilakouser7975]

thanks a lot.......respect from Pakistan

[@MariosMathTutoring]

You’re welcome Nabila!

[@thomasfotiii4363]

You deserve more views

[@MariosMathTutoring]

Thanks Thomas Foti! Glad you like my videos and channel!

[@aidanduffield5395]

I noticed that when you were writing the double negatives (five minus negative five) you had two negatives next to each other, but the negative next to the five was higher up. Is this correct notation if I was wanting to be completely correct with a test? If it is, I like it.

[@MariosMathTutoring]

That’s a good question Aidan... I’ve always written it like that so the minus sign and the negative don’t blend into one line at the same level and throw me off....I’ve seen it written in textbooks that way as well...but officially I don’t know the answer...often times it will be written 5-(-5) so as to avoid confusion...if you find out the answer report back and let us all know or if someone reading this knows...weigh in on this question...

[@aidanduffield5395]

@@MariosMathTutoring ok, thanks.

[@superrobloxgamer4549]

Good

[@frithjof1113]

Danke

[@MariosMathTutoring]

You’re welcome!

[@a.e.r.9898]

bro thanks

[@MariosMathTutoring]

Your welcome!

[@eltasho291]

Thanks Mario, I'm gonna destroy my calculus final.

[@MariosMathTutoring]

You’re welcome! Do well!

[@eltasho291]

@@MariosMathTutoring Thanks again Mario I just passed my final exam of Calculus

[@MariosMathTutoring]

Awesome! Glad to hear you passed!

[@holdenchappell4784]

OK!

[@davidkolivayko2835]

all the calc kids watching this brilliant man before our tests

[@lucashood3337]

U r awesome

[@MariosMathTutoring]

Glad my video helped you Akarsh!

[@navaerick86]

It's like Mario translates Calculus books into English.

[@tcaptain32]

will u be my professor? :)

[@MariosMathTutoring]

Sure! Glad my video helped you.

[@TheNetkrot]

and what is the purpose ??

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julio profe 2.0

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Jeff Bezos teaching me calc!!!

[@joz4738]

😸

[@lgnwyne5308]

B camma...🤣

[@chaelsthumbnailposture3135]

why is this important

[@MariosMathTutoring]

The mean value theorem tells us that between 2 points a and b there is at least one point where the instantaneous rate of change is the same as the average rate of change between a and b.

[@gabbyfazzalari5167]

u made a mistake. took the derivative and 4 is a constant so should be zero

[@spideyyedips6109]

No 💀💀💀