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Question Number 140734 by liberty last updated on 12/May/21
Letm,nbegivenpositiveintegers. Ifx&yarepositivenumberssuchthat x+y=S,Sisaconstant,find thevalueofxandythatmaximize Q=xmyn.
Commented bymr W last updated on 12/May/21
ifmandnbothareeven,thereis minimum. ifonlyoneofm,niseven,thereisno maximumandnominimum. ifbothmandnareodd,thereis maximum.
Answered by EDWIN88 last updated on 12/May/21
settingdQdx=mxm−1(S−x)n−n(S−x)n−1xm=0 weobtainx=mSm+n.Thefirst−derivativetest showthatthisyieldsarelativemaximum andthereforebytheuniquenessofcritical number,anabsolutemaximumwhenx=mSm+n,y=nSm+n
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