A community for students.
Here's the question you clicked on:
 0 viewing
TuringTest
 3 years ago
Mean Value Theorem: is there a typo on the third line?
http://ocw.mit.edu/courses/mathematics/1801scsinglevariablecalculusfall2010/partcmeanvaluetheoremantiderivativesanddifferentialequations/session34introductiontothemeanvaluetheorem/MIT18_01SCF10_ex34prb.pdf
TuringTest
 3 years ago
Mean Value Theorem: is there a typo on the third line? http://ocw.mit.edu/courses/mathematics/1801scsinglevariablecalculusfall2010/partcmeanvaluetheoremantiderivativesanddifferentialequations/session34introductiontothemeanvaluetheorem/MIT18_01SCF10_ex34prb.pdf

This Question is Closed

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.0The paper is drawing a parallel between linear approximations so it talks about switching out \(f'(a)\) for \(f'(c)\) for some specific yet undetermined c but the last formula on the page notes that this idea extended leads to something like a quadratic approximation, which relates to Taylor series\[f(b)=[f(a)+f'(a)(ba)]+\frac{f''(c)}2(ba)^2\]should it not be\[f(b)=[f(a)+f'(c)(ba)]+\frac{f''(c)}2(ba)^2\]or is the whole point using \(f'(a)\)to keep it related to linear approximations?

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.0\[f(b)\approx f(a)+f'(a)(ba)\]near \(x=a\), whereas MVT states that\[f(b)=f(a)+f'(c)(ba)\]for som \(a<c<b\) is the whole point using \(f'(a)\)to keep it related to linear approximations?

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.0reading it again I'm thinking the answer to my own question is "no it's not a typo" (since it says the part in brackets is \(exactly\) the linear approximation, which it is with f'(a) ) but if anyone has any more insight let me know

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.0Never.mind, I think the answer is that it is not a typo. It says the "next term" in the Taylor series will approximate error in an nth degree approximation. I suppose only the next term in the Taylor series would require the c to get an exact equality.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.