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: Increasing/Decreasing composites functions

  1. Oct 12, 2005 #1
    Given that u(x) is always positive and u'(x) < 0, I need to find values of x so that f(x) and g(x) are increasing. f(x) = [u(x)]^2 and g(x) = u(u(x)).

    for f(x) is increasing when f'(x) > 0. so f'(x) = 2u(x) => 2u(x) > 0. would f(x) always be increasing since 2u(x) will always be increasing ( u(x) is always positive, 2u(x) will always be positive as well)?

    and for g'(x) > 0 => [u(u(x))]' => u'(u(x)*(u(x))' = 2u'(u(x))...set larger than 0...since u'(x) is always negative and 2u'(u(x)) is bounded by 2u', does that inequality not hold and so g(x) is never increasing?
    Last edited: Oct 12, 2005
  2. jcsd
  3. Oct 12, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper

    f'(x) is not 2u(x), you need to apply the chain rule. You must also use the chain rule when you analyze g'(x).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook