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 Calculus Calculus Math Forum

 November 11th, 2017, 06:41 AM #1 Senior Member   Joined: Nov 2011 Posts: 250 Thanks: 3 Analysis question Sum of two numbers is 10, what are they if they have the maximum multiplication? [I know the answer, but I need the way to solve it.] November 11th, 2017, 07:41 AM #2 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond Let's call the two numbers $a$ and $b$. Without a loss of generality, assume $a\ge b$. Now take a look at $a^2-ab$. Under what condition is this expression a minimum? Thanks from topsquark November 11th, 2017, 08:09 AM #3 Senior Member   Joined: Nov 2011 Posts: 250 Thanks: 3 I need a maximum. But maybe I am wrong... I think to take this expression ["a square" minus a x b] and equal it to zero. I will fully feel to thank you, for answering, first all, and for your explanation. [if you will give it to me.] Thank you... November 11th, 2017, 08:12 AM #4 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond $$a^2-ab=a(a-b)=0\text{ iff }a=b$$ Form that it follows that $ab$ is maximized. You don't "need" this; it's just one particular approach. November 11th, 2017, 01:59 PM #5 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,838 Thanks: 653 Math Focus: Yet to find out. Maximise $z = x y$ subject to, $x + y = 10$. We could add non-negativity constraints too. From the first constraint, $x = 10 - y$ then $z = (10 - y)y$. $z_y = 10 - 2y = 0 \implies y = 5$ Thus $x = 5$ also. See here: https://www.desmos.com/calculator/fsahli3jgy Tags analysis, question Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Haz5069 Complex Analysis 1 December 3rd, 2016 01:07 PM maximus101 Calculus 0 February 4th, 2011 05:48 AM maximus101 Calculus 0 February 4th, 2011 05:19 AM seams192 Real Analysis 5 May 13th, 2010 09:03 AM airline Calculus 1 September 12th, 2009 10:39 AM

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