Youve Wonderfully put it sir. Cleared all the nuisance that dumped into my brain from other videos. You made me awakening to the MVT. Thank you. Keep Going
Here's a very cool proof, just rotate it by enough degrees that the slope of the line intersecting the interval becomes parallel to x-axis. Now it's the same as Rolle's theorem, which is easier to prove and more intuitive.
Thanks for putting this video up - very clear and concise. Quick question - why use h(x), the distance between the secant line & the function? What's the relationship of h(x) to proving that there exists a c in (a,b) s.t. the secant line is equal to f'(c)? Thanks
because i think since at h(a) = 0 and h(b) =0. we know that h(x) intercepts the x-axis twice and since any curve that intercepts the x-axis twice (according to Rolle's Theorem ) there will be some point "C" between ( a,b ) where h(c) will be 0.
9 years later, by far the best video on proof of this theorem. Thank you.
Short, concise, and well explained, without compromising vital details.
Perfect!! In class we didn't discuss why we were doing things, the vertical distance, equation of the secant line, etc. This explains it!!
The proof is intuitive and elegant; you definitely deserve the applause.👏
I instantly gave this a thumbs up right after I've heard that english accent I was hoping for
I wouldn't say it better!
best video on mean value theorem!
pls upload one on cauchy's MVT too..!
Youve Wonderfully put it sir. Cleared all the nuisance that dumped into my brain from other videos.
You made me awakening to the MVT. Thank you. Keep Going
Tq so much sir.. lots of love from india🙏
This is so clear (decided to watch a video after most of the sites don't have the explanation I was looking for)! Thank you so much!
Finally, I can understand the proof of this theorem. Thanks a lot!
Thank you for taking the time to leave a comment. I appreciate your support.
😮awesome, without loosing a single details. 👍
Thank you
i did find this helpful, James. Thank you 🥰🥰
Mind blown 🤯! Thank you, this video finally made it all click together!
Excellent! Simply AMAZING! Well done, hope you are a teacher!
Is there any known way to prove this theorem without Rolle's theorem? The tought crossed my mind.
you are SO HELPFUL. thank you so much. you explain things so clearly.
The idea that f(x)-h(x) which is substracting the secant line equation from the original function helped me a lot (θ‿θ)
Excellent sir 👏👏👏
awesomely explained.... you are superb... great job
Superb bro excellent explained
Excellent sir
You are excellent.
10/10
in italy we call this Lagrange's Theorem. Good job with the video by the way!
russia 2
Here's a very cool proof, just rotate it by enough degrees that the slope of the line intersecting the interval becomes parallel to x-axis. Now it's the same as Rolle's theorem, which is easier to prove and more intuitive.
Thanks for putting this video up - very clear and concise. Quick question - why use h(x), the distance between the secant line & the function? What's the relationship of h(x) to proving that there exists a c in (a,b) s.t. the secant line is equal to f'(c)? Thanks
because i think since at h(a) = 0 and h(b) =0. we know that h(x) intercepts the x-axis twice and since any curve that intercepts the x-axis twice (according to Rolle's Theorem ) there will be some point "C" between ( a,b ) where h(c) will be 0.
Excellent video. Thank you, and keep up the good work.
God bless you for your good works
Wow, this was such an easy proof. Amazing, thank you!
Glad you liked it!
Very clear explanation. Thank you.
Nicely done ..👍
finally made sense, Thank you!!
Please explain the point g(x) & h(x)
how the actual hell is the vertical distance between f(X) and g(x) equal to 0... and this serves a premise for h(a)=h(b)?
Because the points of intersection of f(x) and g(x) are at x = a and x = b. Since h(x)=f(x)-g(x), it follows h(a)=h(b)=0.
I don't understand why there are some value c in between a and b where h'(x)=0.
can you please make video on proof of taylor's theorem?
To prove Taylor's theorem you just have to aply Cauchy's rule over and over (calculating the derivatives).
Thank you for doing this
Thenk youuu! You're amazing...
This was helpful. Thank you :)
A+
Thnx
thank you
THANK U