Concavity

[2RIP]

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!

[ircdan]

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.