A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing


  • 3 years ago

Lecture 14: MVT proof is incomplete? Moving parallel line up and down to find where it's a tangent to the curve is intuitive, sure, but that doesn't constitute a proof, does it? How do we *know* it will *always* become a tangent, for all possible curves? However intuitive it is, it isn't proven here. Unless I'm missing something?

  • This Question is Open
  1. jkristia
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm not sure if this is correct (and I have not watched that lecture), but I think MVT is an extension to Rolle's theorem which states (something like), if you have 2 points on a curve a an b and f(a) = f(b), meaning a horizontal line from a to b. Then there must be at least one point 'c' on the curve where the tangent line is horizontal too, meaning the derivative is 0. Now if you slant the line between a and b, then the tangent line at 'c' will have the same slope as the slope a-b.

  2. anonymous
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It's the extension of the Rolle's theorem. Draw a curve,|dw:1371142343381:dw| A: (a,f(a)) B: (b,f(b)) g(x) is the line, \[g(x) = f(a) + \frac{ f(b)-f(a) }{ b-a }(x-a)\] Then we can construct another function h(x) = f(x) - g(x) \[h(x) = f(x) - (f(a) + \frac{ f(b)-f(a) }{ b-a }(x-a))\] Then use Rolle's theorem h(a) = h(b) = 0, so there must be a c h'(c) = 0 That's the proof, hope you like it

  3. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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...


  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.