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.
247
likes1233 views
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
4.4106 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.
Frequently asked questions (FAQs)
\(\sqrt[3]{x^3 - 8}\) represents the cube root function. When solving this equation, we find that the value of \(x\) is equal to \(2\) for any real \(x\).
+
Find the derivative of f(x) = 3x^4 - 2x^3 + 7x^2 - 5x + 1.
+
What is the average score of a class in a Math test if 4 students got 80, 5 students got 90, and 3 students got 95?
+
New questions in Mathematics