Question

A record club has found that the marginal​ profit, Upper P prime (x )​, in​ cents, is given by Upper P prime (x )equals negative 0.0008 x cubed plus 0.35 x squared plus 45.5 x for x less than or equals 400​, where x is the number of members currently enrolled in the club. Approximate the total profit when 240 members are enrolled by computing the sum

Answer 1

The total profit when 240 members are enrolled is:

3,587,212.8 cents

Explanation:

First of all, the total profit function is gotten by integrating the marginal profit function.

Integrate thus:

Total Profit = P(x) = [-0.0008x^4 ÷ 4] + [0.35x^3 ÷ 3] + [45.5x^2 ÷ 2]

P(x) = 0.0002x^4 + 0.1167x^3 + 22.75x^2

Next, substitute 240 for x, in the total profit function.

P(x) = 0.0002[240]^4 + 0.1167[240]^3 + 22.75[240]^2

P(x) = 663552 + 1613260.8 + 1310400

P(x) = 3,587,212.8 cents

Equivalent to $35,872.128