My Math Forum Product of 2 convex functions

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 June 22nd, 2012, 04:11 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, 01:11 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: $(fg)''= f''g + 2f'g' fg'#39;$ Now we just need to answer when $(fg)'' \geq 0$? 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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# multiplication of two positive convex functions

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