Intro Real Analysis, Lec 16, Part 1: Mean Value Theorem: Statement, Basic Examples, and Proof

Introductory Real Analysis, Lecture 16, Part 1.

(0:00) Upcoming schedule.
(1:32) Statement of the Mean Value Theorem, visual interpretation, basic examples to consider.
(12:04) Deconstruction of the proof, starting with the use of Rolle's Theorem.
(20:44) Quickly run through the proof again.
(22:24) Sketch the proof of Rolle's Theorem.
(28:53) Sketch the proof of Fermat's Theorem.

Bill Kinney, Bethel University Department of Mathematics and Computer Science. St. Paul, MN.

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[drewjackson]

Love the video! Very informative with great intuition and visual examples to motivate the proofs

[jonaskoelker]

I think the proof of the MVT becomes both easier and more elegant if you cut it into three parts:

1. Rolle's theorem.
2. If f and g are continuous on [a, b] and differentiable on (a, b) with f(a) = g(a) and f(b) = g(b) there exists some c in (a, b) such that f'(c) = g'(c) [proof: apply Rolle's theorem to f - g]
3. The MVT: choose g to be the secant line.

[mananagaraj]

this video was really useful! I study Real Analysis as a part of bachelor's in engineering in Rome, Italy. The methodology of teaching and the material used here just makes the easiest topics really complex.. But in this video, its so simple! Can you please tell me which book he is referring to for Real Analysis?

[chasr]

wow, nice job with the proofs. I'm impressed.
It looked like you were winging with that Fermat theorem. Could that really be true?

[youssephfofana]

I'm ME major. Was this an introductory to Real Analysis or Real Analysis I or II.???
Thanks.