A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
if f is differentiable on [a,b] and f' is decreases strictly on [a,b] prove that
f'(b)<(f(b)f(a))/(ba)<f'(a)
anonymous
 3 years ago
if f is differentiable on [a,b] and f' is decreases strictly on [a,b] prove that f'(b)<(f(b)f(a))/(ba)<f'(a)

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I 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. \[ f'(x_0)= \frac{f(b)f(a)}{ba} \\ \text{if} \ f'(x_0) < 0 \ \text{and} \ ba<0 \ \text{then} \\ f'(x_0)(ba) < 0 \\ \therefore \ f(b)f(a)<0 \\ \therefore \ f(b)<f(a) \] Maybe this helps you with your problem.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0note that the second line is the definition of a strictly decreasing function.
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.