Mean Value Theorem | MIT 18.01SC Single Variable Calculus, Fall 2010

Mean Value Theorem
Instructor: Christine Breiner
View the complete course: ocw.mit.edu/18-...
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@georgesadler7830]

The Mean Value Theorem is one of the great theorems from Calculus. Professor Breiner uses this theorem to solve a classic problem in Calculus. Applying this classic theorem is very helpful.

[@maymkn]

But why do you sound like ChatGPT?

[@GREJFilmsLtd]

For the BC Calc students at Lawrenceville:
Ms. Briener is using the "derivative" from of the MVT in the interval [a, x], instead of the classice [a,b]. So, she re-wrote:
f'(c) = { f(x) - f(a) } / (x - a )
as
f(x) = f(a) + f'(c)*(x - a)
Note, also, this looks like the "linear approximation" of f(x) near x=c !!!

[@hardcorervdhard2kill94]

what is ur life status now after 10 years man?🙂

[@Goose____]

@@hardcorervdhard2kill94 hopefully doing well

[@maryamgholinasab4531]

the greatest way to explain MVT thank you

[@cambium0]

This proof is more satisfying since we don't modify what is to be proved, but maybe more time consuming than applying the first corollary of MVT. The first corollary says if f'(x) > 0 over the interval then f(x) is increasing over the interval and so if we can set the start of the interval at zero (f(0)) and establish that that *equals* zero, we know the rest of the function is > 0 over the interval. In this approach we define the function as f(x) = tanx - x. So we have tanx -x > 0 for 0

[@maymkn]

This is a more intuitive approach. Exactly what I thought on seeing the question.

[@desireelim5287]

This was so helpful, thank you!

[@jesuisravi]

you didn't give us enough time!

[@enistein]

bro dunno the pause button💀💀

[@the_eternal_student]

I did not hear you say what the mean value theorem is.

[@dinithisahanika7823]

❤

[@kenichimori8533]

Proof Point Optical Position P = OP

[@barancel11]

thank you

[@kenichimori8533]

Proof Point And Line P 0 = L 0.
Zero Space Optical Point Equally.

[@ChallHatt]

She gave me time to solve the problem
I did it ...
Now I don't want to watch ahead

[@kenichimori8533]

Somephere cosmenity x y straight line q plus p plus
P = Q(x,y) Plane Degree Pointive Proof.

[@kenichimori8533]

Proof Point Equal Even Space Geometry Minus Point Plus ≠
P = P

[@fedophile]

I'm in love with you Christine Breiner, marry me?