Rolle's Theorem

Calculus: We state and prove Rolle's Theorem - if f(x) is continuous on [a, b], f is differentiable on (a, b), and f(a) = f(b), then there is an x in (a, b) with f'(x) = 0. The examples of (a) f(x) = x^2 -5x + 6 on [2, 3], and (b) f(x) = sin(x) on [pi/4, 3pi/4] are given.

[AnArrogantFrog]

Thank you for being a person that makes these videos. I am in Calculus 1 as a math major and I understand the steps of the problems but I really did not grasp WHY you did this, which will probably be important for me to know in II, III and advanced calculus. Thank you very much for your help I understand that you yourself do not get much out of making these videos but you certainly help a lot of people.

[Zaryn]

I actually like how you had everything written out ahead of time in this video. Instead of waiting for you to write it out, I can see what you're talking about as you're talking about it. And on an accessibility note, the fact that you face the camera and speak clearly probably helps out deaf students who can lip read -- they wouldn't be able to get that from videos that do the work while talking off camera about it.

[MathDoctorBob]

Thanks for the comment. Some people need to watch the problem unfold, but I think one advantage of video is that we can remove much of the wasted time in a lecture. Then one can pause and rewind according to needs.

Facing front not only helps deaf students, but also those with English as a second language. This is why I hate speaking on the phone; I can't see what they are saying. - Bob

[MathDoctorBob]

@AnArrogantFrog You're welcome, and thanks for the comment! It is tough to get a feel for Rolle's Theorem and the Mean Value Theorem on the first exposure. They only show us that something can be done - they don't give guidance on actually finding the solution. On the other hand, this abstraction puts MVT at the heart of many proofs in Calculus.

[mobe]

Thanks for posting this video Bob!! You are well prepared and easy to follow, this has been a great help to me :)

[MathDoctorBob]

You're welcome, and thanks for the kind words! Glad to be of help.

[MathDoctorBob]

Thanks! I have you covered for Calc II. The playlist is not as complete as Calc 1 yet, but getting there. - Bob

[MathDoctorBob]

@evfran2 Sorry it doesn't work for you, but I'm sure there's a math channel out there that does. Admittedly I'm still finding my way on these earlier videos. - Bob

[evfran]

@MathDoctorBob
I just wanted to give you feedback, I find that is the problem with most student or at least my friends, the fact that it is difficult to see what the profs talk about but if you show the work its easy to follow up...anyways thanks for posting these videos I'm sure its helped some one and I'm sure someone appreciates it.

[MathDoctorBob]

@evfran2 Thanks for the follow-up! Early on, I was advised to try to face the camera whenever speaking, which works for documentaries but makes for awkward teaching videos. While I don't trust my handwriting to be clear enough live, I make sure to point at every step on the board now. - Bob

[evfran]

you should instead of just narrating whats going, show the work. This video did not really help me at all because I cant see what your talking about.