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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.

Expert avatar
Jayne
4.4
106 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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