A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing


  • 5 years ago

Why does a function being well defines and it having a point c where lim_|x->c|{((f(x)-f(c))/(x-c)^2}=A < 0 guarantee that f'(c) exists and that c is a maximum point?

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

    I believe I understand the 2nd part of it. Since the bottom of the limit is positive at all times, and the result is negative, that means that f(x)-f(c) is negative on both sides of the limit and use that to prove that f(c) is a maximum point. What I'm really stuck on is proving differentiability. I'll repost the limit with symbols:\[\lim_{x \rightarrow c}(f(x)-f(c))/(x-c)^2 = A < 0\]

  2. 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.