Final answer:
In this case, the rate of change in the cost of running the train for the average speed of 30 km/h is 20.
Therefore, the answer is (B) $20/h.
Step-by-step explanation:
To find the rate of change in the cost of running the train for the average speed of 30 km/h, we need to calculate the derivative of the cost function with respect to the speed variable.
1. Given the cost function C(v) = v² - 40v + 30, where v represents the speed of the train.
2. To find the rate of change in the cost, we need to calculate the derivative of the cost function with respect to v, denoted as dC/dv.
3. Take the derivative of the cost function C(v) with respect to v:
dC/dv = 2v - 40.
4. Substitute the average speed of 30 km/h into the derivative equation:
dC/dv = 2(30) - 40
= 60 - 40
= 20.
5. The rate of change in the cost of running the train for the average speed of 30 km/h is 20.
Therefore, the answer is (B) $20/h.
Your question is incomplete, but most probably the full question was:
Assume the cost function as C(v)=v²-40v+30.
Find the rate of change in the cost of running the train for the average speed: 30km/h−1.
A) $15/h
B) $20/h
C) $25/h
D) $30/h