A company's profit P(x) (in thousands of dollars) from selling x units of a product is given by P(x) = 5x - 0.1x² - 50. What is the marginal profit when 30 units are sold?

Core Concept

The marginal profit is the derivative of the profit function. P'(x) = 5 - 0.2x. At x = 30, P'(30) = 5 - 0.2(30) = 5 - 6 = -1. Since P(x) is in thousands of dollars, the marginal profit is -$1,000. This means that selling the 30th unit actually decreases the profit by $1,000. Option A is incorrect because it's the absolute value of the correct answer but ignores the negative sign. Options C and D are incorrect because they don't properly calculate the derivative and evaluate it at x = 30.