Question
a tractor's fuel consumption depends, among other things, on the tractor's speed. under certain conditions, a tractor's fuel consumption can be described by f(x) = 0.0010x^2 - 0.040x + 0.92 x > 0 where f(x) is fuel consumption in liters/km and x is the tractor's speed in km/h. Determine at which speed the fuel consumption is lowest according to the model.
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Answer to a math question a tractor's fuel consumption depends, among other things, on the tractor's speed. under certain conditions, a tractor's fuel consumption can be described by f(x) = 0.0010x^2 - 0.040x + 0.92 x > 0 where f(x) is fuel consumption in liters/km and x is the tractor's speed in km/h. Determine at which speed the fuel consumption is lowest according to the model.
Jayne
4.496 Answers
Lösning:
Att hitta den/de kritiska punkterna,
f^{\prime}\left(x\right)=0,0020x-0,040=0
0,0020x=0,040
x=20
Kontroll genom andra derivattest,
f^{\doubleprime}\left(x\right)=0.0020>0
Därför är den kritiska punkten ett lokalt minimum.
Eftersom funktionen är kvadratisk är det lokala minimumet också det absoluta minimumet.
Svar: Bränsleförbrukningen är som lägst när hastigheten är 20 km/h.
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