June 22nd, 2012, 05:11 AM  #1 
Senior Member Joined: Apr 2012 Posts: 106 Thanks: 0  Product of 2 convex functions
Hi, how would you prove that the product of two increasing convex functions is also convex? 
June 23rd, 2012, 02:11 PM  #2 
Senior Member Joined: Apr 2012 Posts: 106 Thanks: 0  Re: Product of 2 convex functions
Ok. I returned back to this exercise after 2 day. Here is the solution: Now we just need to answer when ? So it is obvious, that f'' and g'' are positive, f',g' are positive because we have 2 increasing functions  and we shall not forget that g and f have to be positive. 

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convex, functions, product 
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