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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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    $Y$ou'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.2012-06-11

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$x+y=5$, 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 $xy^2$...it doesn't matter).

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