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I don't understand the question at all. It is very confusing. Can anyone help?

The sum of two positive numbers is 5. Find the numbers such that: a. Their product is a maximum. b. The sum of their squares is a minimum. c. The product of one number and the square of the other will be a maximum.

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Let the numbers be y and 5 - y. Then, your problems are a] Maximize y(y-5) s.t. y>=0 b] Minimize y^2 + (y - 5)^2 s.t y >= 0 c] Minimize y^2(y-5) s.t. y>=0. Can you solve them now? – TenaliRaman Jun 11 '12 at 4:52
There are 3 separate problems here. – copper.hat Jun 11 '12 at 5:06
What is it that you find confusing? Lots of folks can help you solve problems here, but that won't help you if you don't explain what it is that you find baffling. – copper.hat Jun 11 '12 at 5:12
You've posted 8 questions within the last 24 hours. All of them are about finding extremes using derivatives, all labeled as homework. Please note that we are not a homework-solution service; if you are having this much difficulty solving these problems, then there is a much more serious problem with your understanding and you need to be reviewing the general ideas, not asking for solutions to specific problems. – Arturo Magidin Jun 11 '12 at 16:01

$x+y=5$, so $y=5-x$. For (a), maximize $xy=x(5-x)=5x-x^2$. For (b), minimize $x^2+y^2=x^2+(5-x)^2=2x^2-10x+25$. For (c), maximize $x^2y=x^2(5-x)=5x^2-x^3$ (or $xy^2$ doesn't matter).

(Do bear in mind in each part that $x,y>0$.)

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