A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Why did we have to say f is continuous on [a,b] and differentiable on (a,b) when we could just say f is differentiable on [a,b] (which implies f is continuous on [a,b])

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I see that a lot in Calculus

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

    and in Real Analysis

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

    The first way says that its continuous on the whole interval but only differentiable on the open interval, so not at the end points. However, the second way "f is differentiable on [a,b] => f is continuous on [a,b]" is saying that its both differentiable and continuous on the whole interval. As for why it matters that its differentiable only on the open interval, not the closed, I can't say.

  4. 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...

23

  • 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.