An entrepreneur starts new companies and sells them when their growth is maximized. Suppose that the annual profit for a new company is given by , where P is in thousands of dollars and x is the number of years after the company is formed. If she wants to sell the company before profits begin to decline, after how many years should she sell it?

Question

An entrepreneur starts new companies and sells them when their growth is maximized. Suppose that the annual profit for a new company is given by  , where P is in thousands of dollars and x is the number of years after the company is formed. If she wants to sell the company before profits begin to decline, after how many years should she sell it? ​

Quizplus · Accepted Answer

To find the optimal selling point, we need to find the maximum point of the function. We can do this by taking the first derivative of the function and setting it equal to zero:

P'(x) = -0.1x^2 + 1.1x - 1 = 0

Solving for x, we get x ≈ 5.5. This means that the maximum profit occurs after approximately 5.5 years.

Since we can't sell half a year of profits, we should round down to the nearest whole year and sell after 5 years, which is answer choice B.

An Entrepreneur Starts New Companies and Sells Them When Their