Real Analysis, Lecture 24: The Derivative and the Mean Value Theorem

[@dopplerdog6817]

I do wish they had put up their videos for analysis 2.

[@BlackTigerClaws]

Damn. That was a *mean* theorem he laid out there.

[@jinks908]

The remark at 47:21 about being “strictly increasing” is incorrect. Just because f(b)>f(a) that doesn’t mean f is strictly increasing on (a,b). It may increase from, say, a to c, then decrease from c to d, and finally increase again from d to b. Thus f(b) may be a higher point on the graph than f(a) while there are still points in between which lie lower than f(a). I honestly think he may have just misspoken since all he is trying to show here is that if f(b)>f(a), then f’(x)>0.

[@ldb579932]

At the last part of the lecture h(x) is the difference in area. Seem it should be [f(b)-f(a)][g(x)-g(a)] - [g(b)-g(a)][f(x)-f(a)] instead. h'(x) is the same as h'(x) in the lecture so the proof still works.

[@klevisaliaj9452]

I agree

[@lazywarrior]

clearly, you are right.

[@a260283]

Topology isn't even taught at my university, and while some of this stuff is From first semester Calculus, many of the Metric space concepts etc. are clearly not. Great Series on Analysis though. I have been following it all the way through.

[@jameelah2881]

Thank you!! These videos are so helpful since my lectures aren't recorded

[@davidmachorro6058]

Does anyone know where can I find the exercises from Chapter 5 that were assigned? As of right now, on the webpage, the last homework only contains exercises from chapter 4.

[@martinspage]

at 55:00 For Rolle's theorem, doesn't c have to be in the open (not closed) interval (a, b) ? And does f(a) have to equal f(b) ? Thanks.

[@tsgoten]

I think you are right about it being an open interval. The only case I can make for the lecture is that he stated it as a "local maximum," so in that case it could just be a closed interval. And yes, f(a) has to equal f(b) for Rolle's Theorem to apply. Which does not require c to be a local maximun.

[@IIAOPSW]

Can you prove the mean value theorem using the intermediate value theorem? If you simply prove the slope of the secant from f(a) to f(b) is in between f'(a) and f'(b), then it follows there is a c such that f'(c)=the slope of the secant.

[@zxcvbs]

Muy bien explicado,I always have the intuition that the book is laughing on my back.

[@samahassan8312]

can you also tell properties of differention of a function in real anylasis course?

[@Fatooshafull21]

is there any one who knows about some Real Analysis Videos,, but from R^p to R^q instead of Real valued functions ?

[@sakhawatali526]

Excellent deliver lecture sir

[@yku01993]

Thanks a million times!

[@michaellewis7861]

Just trichromy? Brilliant?

[@katherineholyfield6485]

i can't wait to use all this in a real world situation

[@beback_]

WHAT? THE REAL WORLD IS FOR UNIMAGINATIVE PEONS! THIS IS NO REAL MATHHEAD, OFF WITH HER HEAD!

[@HarshilHandoo-cm5gk]

being used 13 years later in my winter semester lol

[@frr]

@fuckshitass911 Look at the other lectures. It's all about analysis. This is just the part where you are taught in Calc 1.