The MEAN Value Theorem is Actually Very Nice

Description:
The mean value theorem formalizes our intuition that for "nice" function, you can find places where the tangent line has the same slope as the secant line.
Learning Objectives:
1) State the Mean Value Theorem, including the conditions.
2) Construct examples demonstrating the necessity of the conditions in the Mean Value Theorem.
Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!
Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.
This video is part of a Calculus course taught by Dr. Trefor Bazett at the University of Cincinnati.
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[@jesselam5867]

So good! You are so underrated, best explanation yet. Literally took me two minutes to understand

[@mohammadfallahzade2110]

You mean a lot to us
Best teacher on the planet
thank you

[@jeaniebottleqwerty9433]

Thank you! Cramming hard rn and your enthusiastic explanation is giving me hope and understanding.

[@hatmanchills]

It is really helpful
The true imagination of calculus 👌👌

[@candykiss024]

Amazing and helpful visuals. Thank you

[@DrTrefor]

Glad you liked it!

[@ycombinator765]

4:54 Professor could you please clear it a bit as if why cant a corner point be used to calc derivative?
Cant we use limit and aporoximate from both sides using secants? It will be a great help.
Nice explanation tho. Stuck on your channel fo months now!

[@deliveringIdeas]

Are you still wondering?

[@japinder12345]

we can’t find the derivative of a function at a corner in the graph, because the slope isn’t defined there :- since the slope to the left of the point is different than the slope to the right of the point. Therefore, a function isn’t differentiable at a corner

[@evelyntromp789]

You're amazing!! Thank you!!

[@azhankhan9218]

What if we only say that f(x) is differentiable in [a,b] then it will also be continuous in same.( Why do we have to specify both conditions?)

[@shashpalsingh7243]

First, a correction f(x) has to be differentiable in (a,b), the curly brackets mean it can exclude a and b so just between them. Next, you should read japinder chaudhary's response to Pendulum below.

[@fullfungo]

It’s indeed a good statement. Except for a small correction.
If the function is not defined on xb, we can’t use it.
But you can instead say differentiable on (a,b), has a right derivative at *a* and left derivative at *b* . Then it works fine

[@mohannadhisham6271]

Thank you so much for your work!!

[@vaginalarthritis1753]

Good day. I was wondering if the Mean Value Theorem can be used to make approximations of the numeric values for a function that satisfies it. I'm currently doing questions in my text book related to this application and not a lot of videos or classes online cover it. The text i use "sort off" hints at how to approach but I'm not confident in my abilities.

[@srghma]

So how to find c?

[@saurabhsingh-ow7ue]

thank you sir....

[@ashleyjones2691]

Clutch

[@missile4337]

Can you reply to my question? Why the secant or tangent line is called in this name? And how? Please reply!

[@monasalih6782]

Did you know why?

[@xer_t3661]

thank youuu!

[@Leoeoeoeoeoeoeooeo]

Bro thank u sooooooooooooooooooo much. Me speed run calculus 1 in 4days

[@arestis22]

Mint.

[@shyamdas6231]

Thank you ,sir. I hope you are enjoying chess.

[@DrTrefor]

Very much so!