# Applications of the derivative/Related Rates

• Nov 22nd 2008, 03:17 PM
Applications of the derivative/Related Rates
The manufacturer has found that the cost C and revenue R (in dollars) in one month are related by the equation

C= (R^2/450,000)+12,000

Find the rate of change of revenue with respect to time when the cost is changing by $15 per month and the monthly revenue is$25,000

Thx.
• Nov 22nd 2008, 03:21 PM
Chris L T521
Quote:

The manufacturer has found that the cost C and revenue R (in dollars) in one month are related by the equation

C= (R^2/450,000)+12,000

Find the rate of change of revenue with respect to time when the cost is changing by $15 per month and the monthly revenue is$25,000

Thx.

Differentiate both sides with respect to t to get:

$\displaystyle \frac{\,dC}{\,dt}=\frac{R}{225000}\frac{\,dR}{\,dt }$

You are ask to find $\displaystyle \frac{\,dR}{\,dt}$ give that $\displaystyle \frac{\,dC}{\,dt}=15$ and $\displaystyle R=25000$

Can you take it from here?

--Chris