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Find two positivenumbers `x`and `y`such that `x+y=60`and `x y^3`is maximum. |
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Answer» `x+y =60` `rArr " "x=60 -y" "rArr" "xy^(3) =(60 -y)y^(3)` `"Let "" "f(y) =(60-y) y^(3) " "," "y in (0,60)` Let maximizing f(y) let us find critical points `f(y) =3y^(2) (60-y) -y^(3) =0` `f(y) =y^(2) (180 -4y) =0` `rArr " "y =45` `f(45) lt 0 " and " f(45) gt 0.` Hence local maxima at y =45 So `x=15 " and " y=45` |
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