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I need help with this problem. I have no idea where to start and how to get the answer.

Find three numbers such that the first is the sum of the second and third, the second is the square of the third, and the sum of the three numbers is a minimum.

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Let the numbers be $\,x,y,z\,$:$$(1)\,\,x=y+z$$$$(2)\,\,y=z^2$$and we want the minimum of $$x+y+z=(y+z)+z^2+z=z^2+z+z^2+z=2(z+z^2)=:f(z)$$

Well, find the minimum of $\,f(z):\,\,f'(z)=2(1+2z)=0\Longleftrightarrow z=-1/2\,$ and etc.

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    What would be etc.? I'm still a bit confused..2012-06-11
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    You can either use derivatives, as proposed above (*you* asked for this), or else observe that $\,f(z)=2(z^2+z)\,$ is an upwards parabola and thus its vertex is a minimum point...anyway, above is written the point where the derivative vanishes.2012-06-11
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    So then how would I find the two other numbers that answer the question?2012-06-11
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    It's enough you find out the value for $\,z\,$ , as the other two values can be expressed in terms of it...*read carefully* my answer and try to understand it.2012-06-11
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    Okay I get it. Thank you so much!2012-06-11