Profit Function

Question

The total profit (in dollars) from the sale of x answering machines isP(x)=20x−0.7x2−280.

(A) Find the exact profit from the sale of the 26th machine.

Exact Profit on 26th machine = 

(B) Use the marginal profit to approximate the profit from the sale of the 26th machine.

Approx. profit on 26th machine = 

Answer 1

20x^2 -.7x -280

profit on 26th machine

= 20(26)^2-.7(26) - 20(25)^2 +7(25)

= 13,520-18.2 - 12500 + 17.5

= 1,020-.7 = 1,019.3

marginal profit = derivative = 40x-.7 = 40(26)-.7 = 1040-.7 = 1039.3

for the 25th, marginal profit = 40(25)-.7 = 1000-.7 = 999.3

average of 1039.3 and 999.3 = 2038.6/2= 1019.3

exactly the same profit on the 26th