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Krushnaraj Pandya
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Homework Statement
The operating cost of a truck is 12+(x/6) per km, when the truck travels x km/hr. If the driver earns 6 rupees (*or whatever currency your country has) per hour, what is the most economic speed to operate the truck on a 400 km road? Also, due to weather, the truck can travel only between 35 and 60 km/hr
Homework Equations
dy/dx =0 and f''(x)<0 for maxima of a function and vice versa.
speed=distance/time
The Attempt at a Solution
12+(x/6) per km into 400 gives total expense and profit per hour is 6 so 6 into 400/x is the profit, so net flow of money is 6(400/x)-400(12+{x/6}). per hour, This'd be maximum when its derivative is 0, taking 400 common and differentiating gives (-6/x^2)-(1/6)=0 which has no solution, I also don't know how to use the condition that 35<x<60. I'd appreciate some help, thank you