1. Not finding help here? Sign up for a free 30min 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!

How can I show that h(x)=[g(x)]^2 is concave

  1. Nov 16, 2007 #1
    The problem statement, all variables and given/known data
    How can I show that h(x)=[g(x)]^2 is concave upward on an interval if we know that g is positive and is concave upward on the same interval?

    The attempt at a solution
    I know that that g''(x)>0 since it concaves up. But after this step, I'm lost on proving this question. Any suggestions on how I should approach this question??

    Thanks in advance!
  2. jcsd
  3. Nov 16, 2007 #2
    well you want to show that h''(x) > 0 right? so the obvious thing to do should be to differentiate.

    so h'(x) = 2g(x)g'(x)
    now let's do it again

    h''(x) = 2g'(x)g'(x) + 2g(x)g''(x) = 2(g'(x))^2 + 2g(x)g''(x) > 0, wait this means h is concave up, so we're done.

    when you work on a problem, think about what it is you must show, otherwise you will stare at it forever.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?