Ask
your own question, for FREE!
Mathematics
80 Online
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)
Still Need Help?
Join the QuestionCove community and study together with friends!
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.
note that the second line is the definition of a strictly decreasing function.
Can't find your answer?
Make a FREE account and ask your own questions, OR help others and earn volunteer hours!
Join our real-time social learning platform and learn together with your friends!
Join our real-time social learning platform and learn together with your friends!
Latest Questions
sobitter:
Grammar check? Once, there was a girl named Alaida. She was a small-town girl with big dreams of becoming a famous horse rider.
notmeta:
(algebra 1 level) How do I figure out the correlation on a mathematic table?
SsTDOGRednek:
What is the difference bewtween Sin, Cos, and Tan? What are they for? (Triganomet
luhbabyliyahh:
I am looking for a theater script to write can someone help me?
gelphielvr:
(algebra 1) finding the solution to two equations? I have no clue how to solve th
1 hour ago
4 Replies
1 Medal
5 hours ago
11 Replies
2 Medals
2 hours ago
10 Replies
0 Medals
5 hours ago
12 Replies
0 Medals
23 hours ago
6 Replies
1 Medal