My Math Forum Product of 2 convex functions

 Applied Math Applied Math Forum

 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: $(fg)''= f''g + 2f'g' fg'#39;$ 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.

 Tags convex, functions, product

,

,

,

,

,

,

,

,

,

,

,

,

,

,

# multiplication of two positive convex functions

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Azalea Applied Math 0 February 27th, 2014 05:56 AM johnathanfisk Real Analysis 0 May 28th, 2013 06:32 PM Rak Real Analysis 1 December 1st, 2009 09:45 AM frederico Real Analysis 0 April 6th, 2009 12:31 PM vikram Applied Math 0 February 4th, 2009 03:27 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top