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June 22nd, 2012, 04:11 AM   #1
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Product of 2 convex functions

Hi,
how would you prove that the product of two increasing convex functions is also convex?
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June 23rd, 2012, 01:11 PM   #2
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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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