A company is studying the cost of a new project. The total cost C(x) is given by the function C(x) = 1000 + 500x + 20x^2, where x is the number of units produced. If the company wants to minimize the cost, it should produce a number of units such that the derivative of the cost function is

Core Concept

This question tests the student's understanding of optimization and the properties of the derivative. To minimize the cost, the company should produce a number of units such that the derivative of the cost function is zero. Option A is incorrect because producing units while the derivative is positive would increase the cost. Option B is incorrect because producing units while the derivative is negative would decrease the cost, but not minimize it. Option D is incorrect because the derivative is defined for all x.