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27 March, 21:44

Maximize Q = xy^2, where x and y are positive numbers, such that x + y^2 = 4.

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  1. 27 March, 21:50
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    Hello,

    x+y²=4==>y²=4-x

    Max (Q=xy²) = Max (Q=x (4-x)) = Max (Q=4x-x²)

    Q' (x) = 4-2x = 0

    ==>x=4/2=2 = = >y²=4-2=2==>y=√2 since y>0

    Q'' (x) = - 2==>a maximum.
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