Mean Value Theorem

In this video, I explained the concept of Mean Value Theorem using a Polynomial. The instantaneous rate of change at 'c' is equal to the average rate of change.

[@anonymous-ui7il]

I have learnt my entire university module through you. Your passion for mathematics/calculus is infectious. Thank you so much

[@PrimeNewtons]

Thank you for this comment. It's encouraging. Never Stop Learning.

[@Sarah._.s889]

If you could only be our calculus 1 lecturer, then we will give you distinction. Thank you for the videos they are really helpful 🙏❤️

[@risanarehma4789]

Thank you sooo much. Your explanations are spot on. Keep up the great work. ❤

[@LenchoGebisa-yv6fd]

Very good

[@ArdaBatinTank]

thank you a lot, it is a great video. greetings from Turkey!

[@PrimeNewtons]

Thank you.

[@surendrakverma555]

Very good. Thanks 🙏

[@davidbrisbane7206]

The MVT, or as some of like to call it, _The really mean value theorem_

[@user-qv9jt9md8o]

Sir please can you use the mean value theorem if the theorem does not holds

[@PrimeNewtons]

No! You can only use it if the conditions are met.

[@user-qv9jt9md8o]

i mean if the rolls theorem does not holds

[@naturalsustainable6116]

How do we apply this mean value theorem?

[@awrRoman25]

This mean value theorem (Lagrange's mean value theorem) is used to prove Cauchy's mean value theorem, which is used to prove L'Hopital rule.

[@otsofn2453]

So underrated

[@EE-Spectrum]

Is it possible that the two points could be so close that there's no point (c) between them with the same gradient of the line joining the points? I am not certain that there should always be such a point (c).

[@PrimeNewtons]

As long b is not equal to a , there will always be a c between. You might think the points are close but when you zoom in , there are infinitely many points between two boundary points. As long as the function is continuous and differentiable over the interval.

[@EE-Spectrum]

I now understand that once there's a difference between "b" and "a", no matter how small, there will always be a "c" between them.