Find the rate of change of total​ revenue, cost, and profit with respect to time. Assume that​ R(x) and​ C(x) are in dollars.

Question

​R(x)= 55x - 0.5x^2​ , ​C(x)=5x + 20​, when x=40 and dx/dt=30 units per day

1. The rate of change of total revenue is ​$? per day.
2. Find total cost with respect to time.
3. Find total profit with respect to time.

Answer 1

dR/dt = (55 - x) dx/dt
dC/dt = 5 dx/dt
P=R-C, so dP/dt = (50-x) dx/dt
See what you can do with that.