Rolle's Theorem
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- Опубликовано: 25 авг 2024
- This calculus video tutorial provides a basic introduction into rolle's theorem. It contains plenty of examples and practice problems on how to find the value of c that will satisfy the conclusion of rolle's theorem on the closed interval [a, b]. For rolle's theorem to apply to a function, there are 3 conditions that must be met. (1) The function must be continuous on the closed interval [a, b]. (2) The function must be differentiable on the open interval (a, b). (3) f(a) = f(b). If these conditions are met, then f'(c)=0. There were be some number c in the interval [a, b] where a horizontal tangent line will exist.
Introduction to Limits:
• Calculus 1 - Introduct...
Derivatives - Fast Review:
• Calculus 1 - Derivatives
Introduction to Related Rates:
• Introduction to Relate...
_____________________________
Extreme Value Theorem:
• Extreme Value Theorem
Finding Critical Numbers:
• Finding Critical Numbers
Local Maximum & Minimum:
• Finding Local Maximum ...
Absolute Extrema:
• Finding Absolute Maxim...
Rolle's Theorem:
• Rolle's Theorem
________________________________
Mean Value Theorem:
• Mean Value Theorem
Increasing and Decreasing Functions:
• Increasing and Decreas...
First Derivative Test:
• First Derivative Test
Concavity & Inflection Points:
• Concavity, Inflection ...
Second Derivative Test:
• Second Derivative Test
_________________________________
L'Hopital's Rule:
• L'hopital's rule
Curve Sketching With Derivatives:
• Curve Sketching - Grap...
Newton's Method:
• Newton's Method
Optimization Problems:
• Optimization Problems ...
_______________________________________
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Can you please do a video on successive derivatives which don't include numbers. E.g find the nth derivative of Sin(ax+b)😢.
2 years later, you still are the light and salt for my maths exams
Did u fail your exam?
@Su Hyeon kim From where are u?
4 years later for me
What do you mean by light and salt?
@@computerlover9290 salt and light means if you light on a salt the salt brighten like this the teacher is brighten to the student
started watching you in 8th grade for y=mx+b problems, doing calculus now and youre still clutch
It's so MUCH useful to my self-studying calculus !!! Thank you you filling my COVID-19 time to become better!
How are you?? I'm from Iraq and I didn't understand this Roll can you give me some informatoion about this
@@amjidahmed2399 "this Roll" - what Roll? Toilet paper roll? If you want to understand something, try at least Googling it instead of harassing people. Use your brain.
@@ian.ambrose bro chill he’s just asking a question. and he obviously means Rolle’s therom
@@ian.ambrose calm down dumbass
@@aayaanfarooq9427 Yeah sorry it was a joke.
Tommorow is my exam , and it's so helpful , thanks alot Mr organic chemistry 😊
how was your exam?
Prince Equalizer I got an A in calculus .
@@frontback4574 hey, how's your studies going now?
@@mujtabahussain7015 They're almost done and going well , preparing for my last semester exams now and hope to graduate this year.
@@frontback4574 all the best for your future exams😊😊
Even my university teachers couldn’t teach me like this. God bless you bro!
Never seen a teacher who is good as he is 😶 thanks
wish me luck for my exams 🖤
so how did the exam go LOL
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Hie you guys alive?
As I've always said, RUclips should take its hat off before this guy and awards him as TEACHER OF HUMANITY. And gives him ALL HE WANTS: a house, money, etc.....
Professor Organic Chemistry Tutor, thank you for explaining the Full Version of Rolle's Theorem in Calculus One. This is one of the important Theorems in Calculus. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
In calculus rn. This literally made me understand my teachers 30 min lecture in 6 mins….
How do you manage to explain in 20 minutes what my calculous teacher cant explain in an hour?
5 years later and bro always come through🙏
there has never a time that this channel helped me with my college journey
Thank you so much! You explain Rolle's theorem really clearly. I have also recommended my friends to review the theorem by learning from your video.
YOu have just explained in 60 minutes what I have been struggling with for weeks. (I watched your other videos.) Thank you!!!!!
Thank you so much for these videos they’re still very helpful today!
Thank you very much! Your explanations are so thorough!
I love studying mathematics in Chemistry Class. That's exactly what I do in normal classrooms...
Do you like studying physics, mechanics (subcategory of physics), biology and SAT practice problems? He does that also.
@@marcusvergara6193 Yes and he's best in all of them.
Thank you so much for this!!
I missed some of my classes because I was tested positive and obviously I had to take a break. But this really helped me!
i got an A minus in my calculus 1 course because of you. Now I'm in calculus with the same hope of you guiding me in this darkness.
i learned so much in 20 mins from this video than i did in the 1 hour i spent crying over my professors calc notes
6 years later and bro is still carrying our degrees 🙏
If i knew there were great teaching videos like this before my exams i'd have probably scored well . My teachers are so dumb and their classes were soo boring .I didnt learned a bit of anything from their dumb classes.I wish i'd more time to learn from these videos😭😭
Hey, this video is old. Rolle's theorem doesn't work like that anymore. I was shocked when I found out Rolle's Theorem doesn't work anymore. I think it has something to do with South Korea and the bombing that happened in 2025 in Feb.
@@deliveringIdeas lol
Great video like always! Thank you for the help.
Have a 3 percent in calc rn thank you so much dawg!
Lol
Thank you so much sir!
Even before watching this video i am sure that this video is going to be awesome...:)
Seriously your way of teaching is tooo good
This man, he’s like a gift from God
thank you soo much after every lecture im here and make clear wht i`ve learn
@ 2:02 Yeah we can C where it is... lol
haha....so how are you doing after two years Tihomotse Moteme
Thank you from Poland!
Today is my exam and I'm here thanks buddy 💗
15:28 i was very confused, i thought my computer was yelling at me
thank you sooo much! you just saved my student life.
thanks fo this video its very useful to me , its help me study a lot
who said u will be my savior in everything physic chemistry algebra analysis statistics probability like damn ur gorgeous sir 🫡
it was so helpful though im a korean student!! ur better than my teacher
Outstanding to concept clear.
I wanna clarify a thing @ 3:41 we can also say that multiple number of tangents can be drawn at point "c" hence there is no unique tangent at that point so can we say f(x) is not differentiable at c?
you can't have more than one tangent at a point on a curve
If it was up to me, you'd most definitely receive all of my tuition
Love you bro you're light to Many. ❣️❣️🤝🏻
thank you so much....
Series will be more helpful if you will upload videos on - what is continuity and differentibility. And what are their conditions.
Your Disciple.
hes organic chem, people should know that early calculus before watching this
@@winstonava1 this is early calculus he doesn't just do orgo.
why continuous on [a,b] ? why not continuous on (a,b)? and why differentiable on (a,b)? why not differentiable on [a,b]?
please 🙏 explain
You are really great, sir ☺️. Thanks a lot 🥹❤️
thanks
u saved my life
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Its supposed to be continuos on the closed interval and differentiable on the open one.
yeah exactly you are right my dear
Why u saying that?
But that is what mentioned in the video too.
Very helpful
is graphing the function the only way to tell whether it’s diff or cont ?
15:29 was a jumpscare 💀, lovely video though
at 11:19 for the function x*sqrt(4-x), what if the interval is not [0,4] but [0,5]? How can we plot the graph for the complex part?
It wouldn't satisfy Rolle's Theorem since f(0) =/= f(5)
The question is, are we supposed to know how to automatically graph these functions to determine whether the function is continuous or not ?? If so how do I learn that ??
I don't know if I understood your question right, but certain families of functions are *always* continuous for any point in their domain.
Polynomial functions are always continuous, since they are defined in (-infty, +infty).
Rational functions of the form p(x)/q(x) are continuous everywhere except for any x that gives q(x) = 0.
Trigonometric functions are continuous everywhere in their domains. Furthermore, the sine and cosine functions are continuous everywhere.
Exponential and logarithmic functions, afaik, are also continuous everywhere in their domains.
What this entails is that you *don't* always have to graph functions to find out whether they are continuous. You can just recall the domain of the function in question to discuss its continuity.
tomorrow we have M1 exam ....... It's very useful for us
Well i don't have M1 tmrw but I do have my CIA 1 tmrw ,😢
Thank you alot.
Best video I ever sawww
Thanks king❣️
awesome video
My cousin put me on to you… THANK GOD
why is ur name organic chenm when ur teaching maths? luv the video and all, just curious
Your notation for differentiability, at the start, seems quite brave. I'd like to borrow it but I don't think I understand it. How did you come by it? Is it a stand in for a sort of, non strictly, non abelian sequence? I've never seen an ordered pair used that way before.
47 seconds in but I like it already
0:39, ok, set up, but who is setting it up?
Sorry, i have a question about how to distinguish is the equation is differentiable or not😢
bro how could u draw the graph by seeing the eqn !!!
Thanks
Would've been better if you derived the functions to find if they were differentiable instead of just showing the graph. Great vid anyways :)
"You see that point is c"
yas
S
please teach us budans theorem
Soo....a fraction as an exponent will create a cusp?? Thus making it not differentiable?
Lots or love from Pakistan
9:34 how do you know the graph looks like that? Also at 11:18. Can you just use a graphing calculator on tests?
What if the equation is y=1?
Rolles state that there would be at least 1 point c where slope is 0 since y=1 is a straight line, infinite number of points are there where slope is 0 hence rolles theorem hold true
Which application you use for making this video
Plz reply....thanks
And what if there is no interval is given
And we have find interval also.
15:29 lmfaoooo scared the hell out of me
why doesn't f(x) have to be differentiable on the closed interval and only on the open interval?
Did u get the ans?
How to know this function is continuous at [0,5] interval?
Because F(x) is just a regular polynomial equation
Use intermidiate value theorem
At 11:30 mins
How those kind of graphs drwan just from the equation?
Can anyone help me with it
How the second curve not differential on (a b). Can you elaborate more sir🤔
How did you directly know the graph???😢
thx
how to make graphs from those equations????
How i can sketch all type of graph ?
sry sir i have one why you are take +5 for f'(x) sir
Why did you multiply by 2 ?
can you apply this on any question
it would be negative 8/3, you forgot the negative sign when putting this equation: 8-3x equal to 0
dope video
15:28 I felt that...
how we will get to know which graph will be made for which function?
Just give any X (like... -1, 0, 1... ) value and calculate the Y value for X. Now you have Xand Y values which is written in form (X, Y) and plot this point in graph and do the same for other points by giving different values for X
it's good
Why is ur name the organic chemistry ?
because he teaches chemistry also
13:09 [0, 4] should not be differentiable
It's not cuz 4 isn't differentiable. However the theorem states that the function should be differentiable on the open interval (0, 4) and it is.
Yo when did marky mark get so good at chemistry
teach me sensei how do you draw a graph just by looking at the equation 😭