The cost (in $) to drive a car 12000 miles is given by the formula c(p, m) = 120

Question

The cost (in $) to drive a car 12000 miles is given by the formula c(p, m) = 12000 p/m where p is the cost of gasoline in efficiency 5/gal and, and m is fuel efficiency of the car in miles/gal. Interpret C(3, 25) in the context of this problem (include units) Evaluate C(3.25) Interpret c_m (3.25) in the context of this problem (include units) Evaluate C_m (3, 25) Find an expression for the differential, dC, of cost function. Us your expression in part (e) to approximate the change in cost if price of gas increases by $0.25 and the car's gas mileage decreases by 2 miles/gal

Explanation / Answer

C(3,25) would be the cost to drive 12,000 miles if a gallon of gasoline costs 3$ and the car can run 25 miles in one gallon of fuel.

Thus,

C (3, 25) = 12,000 * 3 / 25

= 1440 $

Cm would be the partial derivative of the function with respect to the mileage. Thus, when costs remain the same, Cm would imply the change in the costs of thejourney when the mileage of the vehicle changes.

Thus,

Cm = -12000 * p / m2

Cm ( 3, 25) = -57.6

e)

C (p,m) = 12,000 p/m

dC = partial derivative w.r.t p * (change in price) + partial derivative w.r.t mileage * ( change in mileage)

= 12000/m (dP) - 12000 p/m2 (dM)

f)

dP = 0.25

dM = -2

Thus, change in price

= 12000/25 * (0.25) + (-12000 * 3 / 25 * 25) * (-2)

= 235.2

Hope this helps.

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