Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ziawasim

if f is differentiable on [a,b] and f' is decreases strictly on [a,b] prove that f'(b)<(f(b)-f(a))/(b-a)<f'(a)

  • one year ago
  • one year ago

  • This Question is Closed
  1. Spacelimbus
    Best Response
    You've already chosen the best response.
    Medals 0

    I haven't seen the mean value theorem of calculus this way yet to be honest. However, let me write down what I know about it, maybe it will help you with your problem nevertheless. \[ f'(x_0)= \frac{f(b)-f(a)}{b-a} \\ \text{if} \ f'(x_0) < 0 \ \text{and} \ b-a<0 \ \text{then} \\ f'(x_0)(b-a) < 0 \\ \therefore \ f(b)-f(a)<0 \\ \therefore \ f(b)<f(a) \] Maybe this helps you with your problem.

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

    note that the second line is the definition of a strictly decreasing function.

    • one year ago
    • Attachments:

See more questions >>>

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.