**Let F be the fuel cost per hour and v the speed in km/h.**

**From question,**

**If t is the time taken by train in covering given distance S km and C the total cost for running the train then,**

**For maximum or minimum value of C, \(\frac{dC}{dv}=0\) **

**Also,**

⇒ \(\frac{d^2C}{dv^2}=\) 2400 x \(\frac{S}{v^2}\)

⇒ \((\frac{d^2C}{dv^2})_{v=80} > 0\)

**Hence, C is minimum, when v = 50 km/hour.**