问题标题：
美国微积分问题（懂英语的来）Thecostoffueltopropelaboatthroughthewater（indollarsperhour)isproportionaltothecubeofthespeed.Acertainferryboatuses$100worthoffuelperhourwhencrusingat10milesperhour.Apart
问题描述：
美国微积分问题（懂英语的来）
Thecostoffueltopropelaboatthroughthewater（indollarsperhour)isproportionaltothecubeofthespeed.Acertainferryboatuses$100worthoffuelperhourwhencrusingat10milesperhour.Apartfromfuel,thecostofrunningthisferry(labor,maintenance,andsoon)is$675perhour.ATwhatspeedshouldittravelsoastominimizethecostpermiletraveled?
马菲回答：
Solution:
Letthecostoffuelbex
x∝v³
Letx=kv³,wherekistheproportionality.
Subv=10mi/hr,x=100intox=kv³,
wehavek=100/1000=1/10
So,x=v³/10
Letthetotalcostpermilebey.
Thetimetakenforonemile=1/v.
y=(1/v)×v³/10+(1/v)×675
=v²/10+675/v
dy/dv=v/5-675/v²
Letdy/dv=0
sov³=675×5=3375,
v=15(mi/hr)
d²y/dv²=1/5+1350/v>0
So,whenv=15(mi/hr)
theminimizedcostpermileis
ymin=15²/10+675/15=67.5($)
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