1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Using the Mean Value Thoerem for this Inequality?

  1. Apr 29, 2012 #1
    1. The problem statement, all variables and given/known data

    Let p > 1 and x > y > 0 Use the MVT to prove the inequality

    py^(p-1)[x-y] =< x^p - y^p =< px^(p-1)[x-y]

    3. The attempt at a solution

    The only way i only how to use the MVT is where i already have the function. Do you have to define the function from the problem? Thanks for your help.

  2. jcsd
  3. Apr 29, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, that's exactly what you have to do. Remember the MVT says$$
    f(b)-f(a) = f'(c)(b-a)$$ where ##c## is between ##a## and ##b##. Look carefully at your problem and see if you can't figure out an f(x) that might work. You need f(x) and its derivative in there. And you have x and y instead of a and b. Worry about the inequality signs after you come up with a likely f(x).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook