My Math Forum Showing a Function is Convex

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 February 14th, 2012, 11:22 AM #1 Member   Joined: Mar 2010 Posts: 51 Thanks: 0 Showing a Function is Convex My homework question is to show that the following function is strictly convex. I'm not asking someone to work it out for me, but how do I show it... if I take all second derivatives, this gives me a function for each. Help! $f(x_1,x_2,x_3)=e^{x_1^2+x_2^2+x_3^2}$
 February 15th, 2012, 11:44 AM #2 Newbie   Joined: Dec 2011 Posts: 15 Thanks: 0 Re: Showing a Function is Convex Let g and h be strictly convex functions an g increasing. You can easily show that their combination goh is also strictly convex. In this case $g(x)=e^x$ and $h(x_1,x_2,x_3)=x_1^2+x_2^2+x_3^2$.
 February 16th, 2012, 06:47 AM #3 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Showing a Function is Convex Just in case it's not clear, goh means g(h(x)). The o is function composition.

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