# Math Help - Another application of differentiation question

1. ## Another application of differentiation question

total cost for a bus to run for one hour is 90+(v²/10) .v is speed of the bus..
take "C" as the cost for bus to run 1Km.What is the speed(v ) need for bus to make the cost minimum

Here what i did:
C=[ 90+(v²/10) ] v -this is the cost for bus to run one hour.
Dc/Dv= 90 + 3v³/10
set to zero and solve
v=√-300 O.o

answer has to be 30 as books says
help
thanks

2. ## Re: Another application of differentiation question

You're derivative is a bit off

If $\displaystyle C=90v+\frac{v^3}{10}\implies \frac{dC}{dv} = 90+\frac{3v^2}{10}$

I don't think the initial equation is correct either.

3. ## Re: Another application of differentiation question

thanks .
What is the correct initial equation then?