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. R (x) equals2 x , C (x) equals0.01 x squared plus 0.3 x plus 30 , when xequals30 and StartFraction dx Over dt EndFraction equals9 units per day

Step-by-step explanation:

Given the Total revenue R (x) = 2x

Cost C (x) = 0.01x²+0.3x+30 where;

x = 30 and dx/dt = 9units per day.

Rate of change of revenue dR/dt = dR/dx • dx/dt

dR/dt = 2dx/dt

dR/dt = 2 (9) = $18

Rate of change of revenue with respect to time is 18dollars/day.

Rate of change of cost dC/dt = dC/dx • dx/dt

dC/dt = (0.02x+0.3) dx/dt

dC/dt at x = 30 and dx/dt = 9 will give;

dC/dt = {0.02 (30) + 0.3}*9

dC/dt = (0.6+0.3) * 9

dC/dt = 0.9*9

dC/dt = $8.1

Rate of change of cost with respect to time is 8.1dollars/day

Profit = Revenue - Cost

Profit = 18-8.1

Daily Profit = $9.9