Answer
a. Yes, because $P(30)$ can be negative if the cost of the 30 shirts is greater than the revenue from the sales of 30 shirts.
b. Yes, $P'(100)$ can be negative if the profit is decreasing when 100 shirts are sold.
c. If $P'(200) is negative, the fraternity's profit is decreasing. More information is necessary to determine whether the fraternity is "losing money."
Work Step by Step
a. We know that $P(30)$ can be negative if the cost of the 30 shirts is greater than the revenue from the sales of 30 shirts. Because the company will be losing money.
b. We can tell that $P'(100)$ can be negative because if the profit is decreasing when 100 shirts are sold the number will be negative.
c. We know that if $P'(200) is negative the fraternity's profit is decreasing because a negative number means it is less than last time and a positive number means it is more. We know that more information is necessary to determine whether the fraternity is "losing money." because we cannot answer the question.
