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Homework Help: 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.
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